The symmetry of two-photon excited states as determined by time-resolved fluorescence depolarization experiments

A new experimental and theoretical approach is presented for the quantitative determination and assignment of the two-photon absorption tensor of fluorophores dissolved in liquid solutions. Two linearly independent time-resolved fluorescence anisotropies and the two-photon polarization ratio were determined from experiments based on using the time-correlated single photon counting technique. The data were analyzed in a global manner under the assumption of prevailing diffusive molecular reorientations and when accounting for the influence of rapid unresolved reorientations. The method has been applied in fluorescence studies of perylene, two-photon excited at 800 nm. The analysis suggests that the two-photon transition is mediated via vibronic coupling including at least two vibrations of different symmetry, and also that the first singlet excited electronic state acts as a dominating intermediate state.     

Unveiling electronic transitions in three novel chiral azo-compounds using linear and nonlinear circular dichroism: a theoretical-experimental study

Herein, we report on the experimental and theoretically study of the linear absorption, electronic circular dichroism (ECD) spectra, as well as the two-photon absorption circular-linear dichroism measurements of three different chiral azo derivatives in dimethylsulfoxide solution. Using potential energy surfaces and frontier orbital analysis, we established the most stable conformation for each molecule and elucidated their different electronic transitions. Our theoretical calculations allowed us to unambiguously identify the spectral position of such transitions and correlate them with the spectral profiles observed in the two-photon absorption spectra. To further elucidate the characteristics of the main electronic transitions in terms of spectral shape and position, we carried out measurements of the polarization dependent two-photon absorption cross sections and determined the two-photon circular-linear dichroism spectra of these azo dyes.     

Resonance hyper-Raman spectra of zinc phthalocyanine

Hyper-Raman spectra were obtained for zinc phthalocyanine in a dilute pyridine solution at excitation wavelengths that are two-photon resonant with the one-photon-allowed B band (360-380 nm) as well as with the two-photon absorption near 440 nm reported by Drobizhev et al. ( J. Chem. Phys. 2006, 124, 224701 ). In both regions, the hyper-Raman spectra were very different from the linear resonance Raman spectra at the corresponding excitation frequencies. While the resonance Raman spectra show only g symmetry modes, almost all of the hyper-Raman frequencies can be assigned as fundamentals of E u symmetry that also are observed in the infrared absorption spectrum or E u symmetry combination bands. These results contrast sharply with previous observations of highly noncentrosymmetric push-pull conjugated molecules and are consistent with a structure for phthalocyanine in solution that is centrosymmetric or nearly so. The hyper-Raman spectra show different intensity patterns in the two excitation regions, consistent with different Franck-Condon and/or vibronic coupling matrix elements for the different resonant states.     

Excited-state symmetry and reorientation dynamics of perylenes in liquid solutions: time-resolved fluorescence depolarization studies using one- and two-photon excitation

The excited-state symmetry and molecular reorientation of perylene, 1,7-diazaperylene, and 2,5,8,11-tetra- tert-butylperylene have been studied by different fluorescence depolarization experiments. The first excited electronic singlet state was reached through one-photon excitation (OPE) and two-photon excitation (TPE). A 400 and 800 nm femtosecond laser pulse was used for this purpose, and data were collected by means of the time-correlated single-photon counting technique. It is found that the rotational correlation times for each perylene derivative are very similar in the OPE and TPE depolarization experiments. For the determination of the two-photon absorption tensor, a recently described theoretical model has been applied (Ryderfors et al. J. Phys. Chem. A 2007, 111, 11531). It was found that the two-photon process can be described by a 2 x 2 absorption tensor for which the components are solvent dependent and exhibit mixed vibronic character. In the dipole approximation this is compatible with a parity-forbidden two-photon absorption into the first excited singlet state.     

Many-particle spectra and nonlinear polarizabilities of crystals (peculiarities of two-photon absorption)

An expression has been found for the frequency and polarization dependence of the two-photon absorption in the many-particle spectral region (vibronic and two-phonon spectra) of centrosymmetric crystals. The peculiarities of one-photon and two-photon absorption have been compared and the conclusions drawn have been correlated with some experimental results on two-photon absorption.     

Low-temperature anomalies of two-photon absorption in In2O3 nanocrystals incorporated into PMMA matrixes

By using a method of two-photon absorption, it has been observed that monodisperse In2O3 nanocrystals (NCs) with sizes equal to approximately 14-24 nm show significant increase of two-photon absorption at low temperatures. When T = 40 K, the two-photon absorption coefficients for low-sized samples drastically increase, whereas such enhancement for the samples with averaged sizes above approximately 24 nm is not significant. The nondiagonal tensor components give one-order-less two-photon absorption values. A principal role in the observed dependences is played by interface nanolayers, demonstrating substantial contribution of nanoconfined effects. This phenomenon could only be observed in highly monodisperse NCs. Increase of the size distribution substantially suppresses the two-photon absorption observed. For the relatively large nanocrystals, the effects are comparable with those of the bulklike crystals. At the same time, the drastic increase at low temperatures may indicate a substantial role of the phonon subsystem.     

Molecular two-photon spectroscopy with two synchronized tunable dye lasers

Two tunable dye lasers, with differing wavelength and polarization, were synchronized to produce a two-photon spectrum in gas phase benzene. Simultaneous absorption of two photons from one laser beam was precluded by choosing appropriate wavelengths. All possible ratios have been measured for a totally-symmetric two-photon transition demonstrating a strong analogy between two-photon absorption and Raman scattering.     

镧系元素f-f跃迁光谱计算

运用不可约张量算符方法,建立了f-f超灵敏跃迁光谱的计算模型,编制了计算f离子^2s+1L~J能级、约化矩阵元、晶体场Stark能级、晶体场态-态跃迁振子强度及模拟吸收光谱的计算机程序.其中,自由f离子能级计算采用包括双电子与叁电子组态相互作用的二三参数模型,晶体场Stark分裂计算采用单电子轨道近似,用Newman角叠加模型计算晶体场参数.f-f跃迁振子强度计算包括静电诱导偶极跃、配体极化偶极跃、振动诱导电偶极跃迁及磁偶极跃迁的贡献.     

Two-photon state selection and angular momentum polarization probed by velocity map imaging: application to H atom photofragment angular distributions from the photodissociation of two-photon state selected HCl and HBr

A formalism for calculating the angular momentum polarization of an atom or a molecule following two-photon excitation of a J-selected state is presented. This formalism is used to interpret the H atom photofragment angular distributions from single-photon dissociation of two-photon rovibronically state selected HCl and HBr prepared via a Q-branch transition. By comparison of the angular distributions measured using the velocity map imaging technique with the theoretical model it is shown that single-photon dissociation of two-photon prepared states can be used for pathway identification, allowing for the identification of the virtual state symmetry in the two-photon absorption and/or the symmetry of the dissociative state. It is also shown that under conditions of excitation with circularly polarized light, or for excitation via non-Q-branch transitions with linearly polarized light the angular momentum polarization is independent of the dynamics of the two-photon transition and analytically computable.     

Mechanism of polarization-induced single-photon fluorescence enhancement

The single-photon fluorescence (SPF) of IR125 can be enhanced when the laser polarization changes from linear through elliptical to circular [A. Nag and D. Goswami, J. Chem. Phys. 132, 154508 (2010)]. In this paper, we further explain and discuss the physical control mechanism. Our theoretical and experimental results demonstrate that the SPF enhancement can be attributed to the nonresonant two-photon absorption of a higher excited state. We conclude that the SPF intensity involving the nonresonant multiphoton absorption of the higher excited state can be controlled by varying the laser polarization.     

Calculation of two-photon absorption strengths with the approximate coupled cluster singles and doubles model CC2 using the resolution-of-identity approximation

An implementation of two-photon absorption matrix elements using the approximate second-order coupled-cluster singles and doubles model CC2 is presented. In this implementation we use the resolution-of-the-identity approximation for the two-electron repulsion integrals to reduce the computational cost. To avoid storage of large arrays we introduce in addition a numerical Laplace transformation of orbital energy denominators for the response of the doubles amplitudes. The error due to the numerical Laplace transformation is found to be negligible. Using this new implementation, we performed a series of benchmark calculations on substituted benzene and azobenzene derivatives to get reference values for TD-DFT results. We show that results obtained with the Coulomb-attenuated B3LYP functional are in reasonable agreement with the coupled-cluster results, whereas other density functionals which do not have a long-range correction give considerably less accurate results. Applications to the AF240 dye molecule and a weakly bound molecular tweezer complex demonstrate that this new RI-CC2 implementation allows for the first time to compute two-photon absorption cross sections with a correlated wave function method for molecules with more than 70 atoms and to apply this method for benchmarking TD-DFT calculations on molecules which are of particular relevance for experimental studies of two-photon absorption.     

Two-photon MPI spectroscopy of alkyl iodides

The two-photon resonant multiphoton ionization (MPI) spectra of methyl iodide, methyl iodide-d₃, ethyl, propyl, and butyl iodide are reported in the 49 000-55 000 cm^?1 region. Four separate transitions to excited states labeled Δ, Π, Σ, Π in increasing energy are expected in this range which result from the excitation of an iodine 5pπ electron to the 6s molecular Rydberg orbital. Two-photon spectroscopy with its different selection rules and unique dependence on the laser polarization is shown to significantly advance the understanding of these transitions. In particular, laser polarization studies identify a state which is strongly two-photon allowed but absent in the UV absorption spectrum as the Σ state. Rotational contours indicate a large geometry change takes place in this transition. The two Π states appear strongly in both the one-and two-photon spectrum. Polarization analysis confirms their electronic symmetry assignment in addition to distinguishing vibronic bands arising from nontotally symmetric vibrations. No evidence is found for the Δ state in the multiphoton ionization spectrum, due to either a small two-photon cross section or a low probability of ionization following the initial two-photon transition. Further complications and characteristics of single laser MPI spectroscopy in the study of two-photon absorption in methyl iodide and other fundamental molecules are discussed.     

Quantum-classical modeling of nonlinear pulse propagation in a dissolved two-photon active chromophore

In the present work we outline the implications of a quantum-classical approach for modeling two-photon absorption of organic chromophores in solution. The approach joins many-photon absorption dynamic simulations with quantum chemical first principles calculations of corresponding excitation energies and transition matrix elements. Among a number of conclusions of the study, we highlight three: (i) The use of either short- or long-pulse excitation is demonstrated to switch the absorptive capacity of the nonlinear medium owing to enhancement of the nonlinear stepwise processes; (ii) The two-photon cross section strongly depends on the way in which the dephasing rate decays when the laser frequency is tuned off-resonant with the corresponding molecular transition; (iii) The results of the pulse propagation simulations based on electronic structure data obtained with a new Coulomb attenuated functional is shown to be in much better agreement with the experimental results than those based on data received with traditional density functionals.     

Two-photon microscopy and spectroscopy of lanthanide bioprobes.

The linear and non-linear photophysical properties of tris-dipicolinate europium and terbium complexes (absorption, emission, lifetime, luminescence induced by two-photon absorption) are studied in the crystalline state as well as in protein derivative crystals and compared to those in solution. Upon laser irradiation at 532 nm, luminescence of terbium is induced by a two-photon antenna effect, whereas luminescence of europium results from one-photon absorption in forbidden f-f transitions. Finally, linear and two-photon microscopy imaging experiments on biological and bio-inspired crystals are performed. These first proof-of-concept experiments open the way for the development of time-resolved non-linear microscopy that should combine the advantages of lanthanide luminescence (long lifetime, sharp emission bands, insensitivity to oxygen) with those of confocal biphotonic excitation (near-IR excitation, 3D resolution and reduced photodamage).     

Sur la theorie quantique des equations de hartree–fock dependant du temps. IV. Expression matricielle du tenseur d'hyperpolarisabilité

Following a paper drawing up a matrix form of the time-dependent Hartree–Fock equations which allow the calculation of the nth harmonic generation, we establish the matrix form of the hyperpolarizability tensor. In case of linear polarization, we show that, if the ground-state orbitals are real, so are the perturbed ones. This involves an easy expression of the hyperpolarizability tensor.     

Vibronic activity in the two-photon spectrum of pyrene

A CNDO/S Cl calculation of the two-photon vibronic activity of some b_1u and b_2u vibrational modes of pyrene is presented. The two-photon amplitude tensor is discussed in terms of vibronic coupling coefficients calculated by means of the orbital-following method. The results are in good agreement with the experimental data taken from a recently observed two-photon spectrum of pyrene in a Shpolskii matrix. The role of the ground-state coupling with the first excited B_1u state has been investigated and is shown to be responsible for most of the vibronically induced two-photon intensity of the spectrum. The calculations also show that the 1310 cm^?1 (b_1u; observed ground-state value) mode is associated with the largest vibronic coupling coefficients and the strongest two-photon amplitude tensor and therefore must be correlated with the most intense B_1u X b_1u false origin ≈ 1496 cm^?1 from the pure (0-0) line.     

Nonperturbative modeling of two-photon absorption in a three-state system

The physics of the two-photon absorption process is investigated for a three-state system. The density-matrix equations for the two-photon interaction are solved in the steady-state limit assuming that the pump laser radiation is monochromatic. Collisional broadening, saturation, and Stark shifting of the two-photon resonance are investigated in detail by numerical solution of the steady-state density-matrix equations. Analytical expressions for the saturation intensity and the Stark shift are derived for the case where the single-photon transitions between the intermediate state and the initial and final states are far from resonance with the pump laser. For this case, it is found that the direction of the Stark shift is dependent on the relative magnitudes of the dipole-moment matrix elements for the single-photon transitions that couple the intermediate state with the initial and final states. Saturation and Stark shifting are also investigated for the case where the single-photon transitions between the intermediate state and the initial and final states are close to resonance with the pump laser.     

Total characterisation of the excited-state density matrix in laser fluorescence experiments

The axial symmetry of the tensor density matrix elements created by the absorption of linearly polarised radiation is demonstrated. It is shown that a full determination of the state multipoles of a polarised array is possible using a single experimental geometry.     

Two-photon absorption dependence on the temperature for azoaromatic compounds: effect of molecular conformation

This work reports on the effect of temperature on the two-photon absorption cross section of azoaromatic chromophores. A linear decrease in the two-photon absorption cross section with the temperature was observed for several azochromophores. This process was characterized by introducing a two-photon absorption thermal coefficient (ddelta/dT), whose typical values are approximately 2GM/degrees C for all the azochromophores studied here. Such an effect was attributed to thermal induced molecular conformation changes, described by the sum-over-states model and semiempirical calculations, which affect the molecular dipole moments. The characterization of the phenomenon reported here for other nonlinear materials can help in the design of specific applications using two-photon absorption.