Resonant enhancement of two-photon absorption in substituted fluorene molecules

The degenerate and nondegenerate two-photon absorption (2PA) spectra for a symmetric and an asymmetric fluorene derivative were experimentally measured in order to determine the effect of intermediate state resonance enhancement (ISRE) on the 2PA cross section delta. The ability to tune the individual photon energies in the nondegenerate 2PA (ND-2PA) process afforded a quantitative study of the ISRE without modifying the chemical structure of the investigated chromophores. Both molecules exhibited resonant enhancement of the nonlinearity with the asymmetric compound showing as much as a twentyfold increase in delta. Furthermore, the possibility of achieving over a one order of magnitude enhancement of the nonlinearity reveals the potential benefits of utilizing ND-2PA for certain applications. To model ISRE, we have used correlated quantum-chemical methods together with the perturbative sum-over-states (SOS) expression. We find strong qualitative and quantitative correlation between the experimental and theoretical results. Finally, using a simplified three-level model for the SOS expression, we provide intuitive insight into the process of ISRE for ND-2PA.     

Theoretical investigation of two-photon absorption properties for a series of bifluorene molecules

The two-photon absorption (TPA) cross-sections of a series of bifluorene molecules with different substituents (constructing three types of structures D–π–D, A–π–A and D–π–A) were calculated using ZINDO/SOS program. The results showed that the A–π–A structure with strong substituent-nitro had the largest TPA cross-section for these molecules. To verify the results, we analyzed the charge quantity of the ground and the main excited states as well as the frontier orbitals of the investigated molecules. The equilibrium geometries were obtained with AM1 method, and using ZINDO-SOS to calculate the third-order nonlinearities of the molecules, then gained the TPA cross-sections. We found that for the compounds with bifluorene as π center, the donor and acceptor strength are the important factor for the enhancement of the TPA properties, and compared with molecules with fluorene as π center, the large TPA cross-sections of bifluorene are caused by coupling effects between the two monomers.     

Ab initio studies of two-photon absorption of some stilbenoid chromophores

Two-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to second-order response function. Several important issues in modeling are highlighted which must be addressed for a reliable reproduction of the experimental results. It is evident that the correct order of magnitude of calculated two-photon absorption cross sections can only be obtained if proper account is taken of vibrational broadening of the absorption profiles. A comparison of the theoretical results with the experimental ones indicates that the computed two-photon absorption cross sections are in rough agreement with our previous report, although the observed systematic increase of the cross sections with the electron acceptor strength is not well reproduced. It is suggested that this disagreement may be due not only to the deficiencies of the computations but also to a variety of factors contributing to the experimental value of the effective two-photon absorption cross section, which are not taken into account in the ab initio calculations.     

Theoretical study of one- and two-photon absorption properties of pyrene derivatives

The geometrical structure, electronic structure, one-photon absorption (OPA) properties of pyrene and its derivatives have been theoretically studied by using density functional theory (DFT) method and Zerner’s intermediate neglect of differential overlap (ZINDO) methods, and their two-photon absorption (TPA) properties are calculated by the ZINDO/sum-over-states method. The results show that introducing donor groups to pyrene molecule, increasing the number of donor groups, extending the conjugated length, or forming circular conjugated dimer can increase the oscillator strength (f) in the TPA process and ultimately result in extremely large TPA cross-sections and strong OPA around 400 nm of pyrene derivatives. All these results give us some basic principles to design pyrene derivatives with large TPA cross-sections. This shed light into the significance of the pyrene derivatives as promising fluorescent probes in biochemistry when they were linked to some special recognizing groups.     

Strong two-photon absorption in new asymmetrically substituted porphyrins: interference between charge-transfer and intermediate-resonance pathways

We study two-photon absorption (2PA) in two series of new free-base porphyrins with 4-(diphenylamino)stilbene or 4,4'-bis-(diphenylamino)stilbene (BDPAS) attached via pi-conjugating linkers at the porphyrin meso-position. We show that this new substitution modality increases the 2PA cross section in the Soret band region (excitation wavelength 750-900 nm) of the core porphyrin by nearly 2 orders of magnitude, from sigma(2) approximately 10 GM for the meso-phenyl-substituted analogue to sigma(2) approximately 10(3) GM for the ethynyl-linked BDPAS-porphyrin dyad. The 2PA properties are quantitatively described by considering two different and interfering 2PA quantum transition pathways. The first path involves virtual transition via intermediate one-photon resonance. The second path bypasses the intermediate resonance and occurs due to a large permanent dipole moment difference between the ground and the final electronic states. To our best knowledge, this is the first experimental observation of the combined effect of these two pathways on one particular two-photon transition, resulting in quantum-interference-modulated 2PA strength.     

Theoretical study of two-photon absorption properties of a series of ferrocene-based chromophores

The electronic structures, one-photon absorption (OPA), and two-photon absorption (TPA) properties of a series of ferrocene-based chromophores with TCF-type acceptors (TCF = 2-dicyanomethylene-3-cyano-4-methyl-2,5-dihydrofuran) have been studied by using the ZINDO-SOS method. The results have revealed that OPA and TPA of ferrocenyl derivatives are affected by the strength of the acceptor, especially the pi-bridge conjugation length. The TPA cross section increases with increasing acceptor strength and pi-bridge conjugation length. The TCF-type acceptor with a phenyl group can lead to a larger TPA cross section. Quadrupole molecules have the largest TPA cross sections (2000-3000 GM), which are about 4 times that of the corresponding dipolar molecules, indicating larger interactions between the top and bottom branches. Finally, the origins of the two-photon excitations for ferrocenyl derivatives are analyzed. The calculations show that ferrocenyl derivatives with TCF-type acceptors (especially quadrupole molecules) are promising candidates for TPA materials.     

Theoretical study of one-photon and two-photon absorption properties of perylene tetracarboxylic derivatives

The geometrical structure, electronic structure, one-photon absorption (OPA) and two-photon absorption (TPA) properties of the perylene tetracarboxylic derivatives (PTCDs) were studied theoretically by using density functional theory (DFT) and Zerner's intermediate neglect of differential overlap (ZINDO) methods. The results revealed that increasing the number of naphthalene nucleus, extending the conjugated length on long axis, increasing the strength of donor group on lateral side, decreasing the DeltaE(H-L) (energy gap between the highest occupied orbital and the lowest unoccupied orbital) and keeping the conjugation effect and inductive effect along the same molecular axis are the efficient ways to enlarge TPA cross section of PTCDs compounds. The results that PTCDs compounds exhibited extremely large TPA cross section of around 800-1100 nm (near infrared region) shed light into the significance of the PTCDs compounds for applications in TPA labeling materials in vivo.     

酞菁及其不对称取代物的电子结构和非线性光学特 性的理论研究

利用AM1方法计算多种酞菁不对称取代物的电子结构与非线性光学特性,并探讨它们之间的关系。结果表明偶极矩μ,能级差△E~D~A,电荷转移△Q~D~A与二阶非线性光学系数β之间都存在一定的规律性,其中μ与β和△E~D~A与β之间的关系较为明显,并有相似趋势。     

One- and two-photon absorptions in asymmetrically substituted free-base porphyrins: a density functional theory study

Electronic spectra and structures of a new family of free-base porphyrin (H(2)P) derivatives with 4-(diphenylamino)stilbene (DPAS) or 4,4'-bis-(diphenylamino)stilbene (BDPAS) asymmetric substituents, recently synthesized and studied by Drobizhev et al. [J. Phys. Chem. B 110, 9802 (2006)] are investigated by density functional theory (DFT) using modern density functionals and the 6-31G* basis set. The time-dependent DFT technique is applied for calculations of one- and two-photon absorption spectra, electric and magnetic dipole moments, and for prediction of electronic circular dichroism for these chiral molecules. The four-band absorption spectrum of the H(2)P molecule (Q(x), Q(y), 0-0 and 1-0 bands) is enhanced in single-bond-linked DPAS. This enhancement is explained by hyperconjugation of the almost orthogonal pi systems and by small charge-transfer admixtures. The effect is much stronger for the double-bond- and triple-bond-linked DPAS and BDPAS substituents where absorption in the Q region transforms into a two-band spectrum. These molecules with ethenyl and ethynyl bonding of the porphyrin and donor substituent show very strong two-photon absorption in the near-infrared region. DFT calculations explain this by more efficient conjugation between the H(2)P and DPAS (BDPAS) chromophores, since they are almost coplanar: "Gerade" states of the H(2)P molecule occur in the Soret region and transform into charge-transfer states with nonzero transition moments. They are responsible for the strong two-photon absorption effects. Mixing of excitations in both chromophores explains the broadening of the Soret band. Though the calculated two-photon absorption cross sections are overestimated, the qualitative trends are reproduced and help understanding the whole genesis of spectra of these asymmetrically substituted H(2)P derivatives.     

Theoretical investigation of one- and two-photon absorption properties of platinum acetylide chromophores

In this paper, we have theoretically investigated bis((4-phenylethynyl)phenyl) ethynyl)bis(trimethylphosphine)platinum(II) (PE2) and its analogs three platinum acetylide complexes (1-3) that feature highly pi-conjugated ligands (alkynyl-dimethylfluorene substituted with electron-donating or -withdrawing moieties). The geometrical and electronic structures are calculated at the ECP60MWB//6-31G*(H, C, P, N, S) basis set level by the density functional theory (DFT) method; one-photon absorption properties have been calculated by using time-dependent DFT (TDDFT) and Zerner's intermediate neglect of differential overlap (ZINDO) methods, and two-photon absorption (TPA) properties are obtained with the ZINDO/sum-over-states method. The values of beta(sp) and beta(d) for Pt are adjusted to -1 eV and -28.5 eV, respectively, to make one-photon absorption spectra calculated by ZINDO closest to the experimental data and TDDFT results. The calculated results indicate that all molecules in this work (involving cis isomers of molecules 1-3) take on two TPA peaks in the 600-800 nm region. The peak at 700-750 nm should not be simply attributed to the appearance of noncentrosymmetric cis isomers in solution, although trans and cis isomers adhere to a different selection rule. Every TPA peak results from its transition character. Molecules 1-3 show greater two-photon absorption strength compared with PE2 and retain good transparency.     

Theoretical investigation of one-photon and two-photon absorption properties for multiply N-confused porphyrins

We have theoretically investigated a series of multiply N-confused porphyrins and their Zn or Cu complexes for the first time by using DFT(B3LYP/6-31G*) and ZINDO/SOS methods. The electronic structure, one-photon absorption (OPA), and two-photon absorption (TPA) properties have been studied in detail. The calculated results indicate that the OPA spectra of multiply N-confused porphyrins are red-shifted and the OPA intensities decrease compared to normal porphyrin. The maximum two photon absorption wavelengths lambda(max) are blue-shifted and the TPA cross sections delta(max) are increased 22.7-112.1 GM when the N atoms one by one are inverted from core to beta position to form multiply N-confused porphyrins. Especially delta(max) of N3CP get to 164.7 GM. The electron donors -C6F5s at meso-position can make the TPA cross section delta(max) increase. After forming metal complexes with Cu or Zn, the TPA properties of multiply N-confused porphyrins are further increased except for N3CP, N4CP. Our theoretical findings demonstrate that the multiply N-confused prophyrins as well as their metal complexes and derivatives are promising molecules that can be assembled series of materials with large TPA cross section, and are sure to be the subject of further investigation.     

Theoretical investigation of two-photon absorption allowed excited states in symmetrically substituted diacetylenes by ab initio molecular-orbital method

Symmetrically substituted diacetylene compounds, which shows large two-photon absorption (TPA) cross sections, have been theoretically investigated by the ab initio molecular-orbital method employing several theoretical models including the configuration interaction with single excitation (CIS), random phase approximation (RPA), and time-dependent density-functional theory (TDDFT) methods. The calculated excited energies are overestimated by CIS or RPA, whereas underestimated by TDDFT with the B3LYP parametrization for both one-photon absorption (OPA) and TPA allowed states. The lowest OPA state is well described by the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) transition. On the other hand, lower TPA allowed states can be represented as the superposition of the HOMO-LUMO+1 and HOMO-1-LUMO transitions, giving rise to two TPA allowed states. The absorption intensity for the lower TPA state of the diacetylenes molecules is discussed in terms of the alternancy symmetry and its breaking. The symmetry property is differently manifested for neutral and dicationic diacetylenes. Introduction of charges breaks the alternancy symmetry, which gives rise to an increase in the TPA cross sections at the lower frequency. The upper TPA state is calculated to show huge TPA cross sections, which reproduces the enhancement of the TPA cross section experimentally observed for one of the diacetylenes at the higher-frequency region. The enhancement is discussed employing an index defined as the ratio of the transition polarizability and its static limit, which represents the degree of influence of one-photon resonance on the TPA intensity. The huge TPA cross sections are found to be due to a near-resonance effect. The present theoretical calculation approves the previously proposed assumption based on the four-state (dual three-state) model, which consists of the ground, one OPA allowed, and two TPA allowed states.     

Solvent effects on two-photon absorption of dialkylamino substituted distyrylbenzene chromophore

Solvent effects on the two-photon absorption of a symmetrical diamino substituted distyrylbenzene chromophore have been studied using the density functional response theory in combination with the polarizable continuum model. It is shown that the dielectric medium has a rather small effect both on the bond length alternation and on the one-photon absorption spectrum, but it affects significantly the two-photon absorption cross section. It is found that both one- and two-photon absorptions are extremely sensitive to the planarity of the molecule, and the absorption intensity can be dramatically reduced by the conformation distortion. It has led to the conclusion that the experimentally observed anomalous solvent effect on the two-photon absorption of dialkylamino substituted distyrylbenzene chromophores cannot be attributed to the intrinsic properties of a single molecule and its interaction with solvents.     

Theoretical prediction of one- and two-photon absorption properties of N-annulated quaterrylenes as near-infrared chromophores

Graphene nanoribbons (GNRs) have attracted increasing attention due to high potentiality in nanoelectronics. In the present study, quantum-chemical calculations of structural and nonlinear optical properties have been first carried out for the nanoelectronical materials, a new series of ladder-type N-annulated quaterrylenes and their imide chromophores. The effects of the solvent, terminal groups, the number of N-annulated bridges, and π-conjugated length are discussed in detail. The solvent effect is significant on the one-photon absorption (OPA). Moreover, the OPA and two-photon absorption (TPA) properties of the two series of DI and N-MI molecules show a clear solvent dependence, which is attributed to the carboximide substitution featuring larger polarization. Introducing electron-donating groups and dicarboximides and increasing the conjugated length lead to red-shifts of the OPA, emission, and TPA spectra, lower emission lifetimes, and enhanced TPA cross sections (δ(max)), but further extension of the conjugated framework does not always promote an increase of δ(max). The changing trends of δ(max) can be explained by the transition moment and the intramolecular charge transfer. All N-annulated quaterrylene and their imide derivatives possess small energy gaps, intense near-infrared absorption and emission, and large δ(max), which are important for use as two-photon fluorescent labeling materials.     

TDDFT study of one- and two-photon absorption properties: donor-pi-acceptor chromophores

We report a comprehensive time-dependent density functional theory (TDDFT) study of one-photon and two-photon absorption (OPA and TPA, respectively) spectra for donor-pi-acceptor molecules. The calculated excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, although the oscillator strengths were overestimated in some cases. Calculated TPA cross sections applying the two-state approximation were shown to be highly dependent on the form of the line-shape function used. Although a good agreement with experimental TPA spectra was generally observed, the wide range in the experimentally measured values and lack of systematic experimental data on solvent effects limited a detailed comparison as yet.     

Theoretical study of two-photon absorption in donor-acceptor chromophores tetraalkylammonium halide/carbon tetrabromide

Two-photon absorption properties of a series of donor-acceptor chromophores of tetraalkylammonium halide/carbon tetrabromide ([NR4h.CBr4], h = Cl, Br, I; R = Me, Et, Pr) complexes are investigated in terms of the calculated results by the time-dependent density functional theory (TDDFT) technique combined with the sum-over-states (SOS) method. The modeling two-photon absorption spectra show that these charge-transfer complexes have large two-photon absorption (TPA) cross sections and the [NEt4I.CBr4] has the largest TPA cross section delta with the value of 5.0 x 10(-45) cm4 s photon(-1). The maximum values of delta increase with increasing separations between the donor/acceptor in the order Cl...Br < Br...Br < I...Br for [NEt4h.CBr4] complexes; however, the TPA cross sections delta vary slightly as the size of the alkyl group increases from methyl to propyl for the bromide as a donor, and the maximum wavelength of the TPA peak lambdamax indicates a bathochromic shift. The charge transfers from the halide anion to the carbon tetrabromide make a significant contribution to the excited states, and the donor-acceptor charge transfer plays an important role in the TPA activity, whereas changes in size of alkyl group do not make a substantial contribution to TPA.     

Theoretical study of one- and two-photon absorption properties of octupolar D2d and D3 bipyridyl metal complexes

The molecular equilibrium structures, electronic structures, and one- and two-photon absorption (TPA) properties of C2v (Zn(II), Fe(II) and Cu(I)) dipolar and D2d (Zn(II) and Cu(I)) and D3 (Zn(II)) octupolar metal complexes featuring different functionalized bipyridyl ligands have been studied by the ZINDO-SOS method. The calculated results show that one- and two-photon absorption properties of metal complexes are strongly influenced by the nature of the ligands (donor end groups and pi linkers) and metal ions as well as by the symmetry of the complexes. The length of the pi-conjugated backbone, the Lewis acidity of the metal ions, and the increase of ligand-to-metal ratio result in a substantial enhancement of the TPA cross sections of metal complexes. Substitution of C=N and N=N for C=C plays an important role in altering the maximum TPA wavelengths and the maximum TPA cross sections of metal complexes. Of them, the C=N substituted metal complexes have relatively large TPA cross sections. Replacing styryl with thienylvinyl makes the one-photon absorption wavelength red shift and at the same time leads to a great decrease of the maximum TPA cross sections of metal complexes. The possible reason is discussed. In the range 500-1250 nm, octupolar metal complexes exhibit intense TPAs and therefore are promising candidates for TPA materials.     

A critical theoretical study on the two-photon absorption properties of some selective triaryl borane-1-naphthylphenyl amine based charge transfer molecules

In the present work, we have studied the two-photon absorption (TPA) properties of some selective molecules containing triarylborane and 1-naphthylphenylamine as the acceptor and donor moiety, respectively. The calculations are performed by using the state-of-the-art linear and quadratic response theory in the framework of the time dependent density functional theoretical method. The TPA parameters are calculated with CAMB3LYP functional and the cc-pVDZ basis set. The one-photon results indicate that both the electronic transitions (S(0)-S(1) and S(0)-S(2)) are associated with the charge transfer interaction between the donor and acceptor moieties along with the reorganization of the π-electron density. All these chromophores are found to have very strong two-photon active modes. In order to find out the origin of large TP transition probability of these molecules, we have performed two-state model (TSM) and sum-over-states (SOS) calculations. We have found that the TSM failed to reproduce the correct trend of the TP transition probability of the molecules obtained from the response theory, while SOS is quite successful in doing so. The whole study indicates that the transition moments between the excited states play a pivotal role in controlling the TP transition probabilities of these molecules. The role of solvent in the TP transition probability of these molecules has meticulously been scrutinized within the polarized continuum model (PCM). Further more, we have benchmarked our theoretical findings by calculating the TPA cross-section of a boron and nitrogen containing a charge transfer molecule for which the experimental result is available and we found that our theoretical result is in good agreement with the experimental one which definitely demonstrates the potential of all these light-emitting diode molecules as TP active materials too.     

Theoretical insight into linear optical and two-photon absorption properties for a series of N-arylpyrrole-based dyes

N-arylpyrrole-based dyes possessing excellent opto-electronic properties are promising candidates for two-photon fluorescence labeling materials. The systematic investigation of novel N-arylpyrrole derivatives is of great importance for both fine-tuning electronic spectra and designing two-photon absorption (2PA) materials. We thoroughly studied influences of the π-conjugated center and N-substituted pyrrole moieties on the linear optical and 2PA properties. Our results show that introducing N-arylpyrrole produces bathochromic-shifts of the absorption and emission bands and an enhancement of the 2PA cross section (δ(max)), demonstrating that the electron-rich pyrrole moieties can efficiently increase intramolecular charge transfer. Substitution of fluorenyl with benzothiadiazole produces the lower energy gap, higher emission lifetime, red-shift of 2PA spectra and larger δ(max). The absorption and emission bands are highly dependent on the nature of the active building blocks. The aromatic rings attached to pyrrole can modulate the absorption peaks in the high energy and thus subtly modify the electronic properties.