Daniel H. Friese

Pyrrolo[3,2-b]pyrroles—From Unprecedented Solvatofluorochromism to Two-Photon Absorption

A combined experimental and theoretical study of the two-photon absorption (2PA) properties of a series of quadrupolar molecules possessing a highly electron-rich heterocyclic core, pyrrolo[3,2-b]pyrrole, is presented. In agreement with quantum-chemical calculations, large 2PA cross-section values, σ2PA ≈10(2) -10(3)  GM (1 GM=10(50)  cm(4)  s photon(-1) ), are observed at wavelengths of 650-700 nm, which correspond to the two-photon allowed but one-photon forbidden transitions. The calculations also predict that increased planarity of this molecule through removal of two N-substituents leads to further increase in the σ2PA values. Surprisingly, the most quadrupolar pyrrolo[3,2-b]pyrrole derivative, containing two 4-nitrophenyl substituents at positions 2 and 5, demonstrates a very strong solvatofluorochromic effect, with a fluorescence quantum yield as high as 0.96 in cyclohexane, whereas the fluorescence vanishes in DMSO.

Intermolecular charge transfer enhances two-photon absorption in yellow fluorescent protein

We present a quantum chemical study of the two-photon absorption (TPA) properties of yellow fluorescent protein (YFP), a mutant of the extensively studied green fluorescent protein. The aromatic chromophore of YFP has a π-stacking interaction with the aromatic ring of a tyrosine residue (Tyr203) in a parallel-displaced structure with a distance of about 3.4 Å. We study the TPA spectrum of the π-stacking system of YFP using the well-established Coulomb-attenuated B3LYP density functional (CAM-B3LYP) and the second-order approximate coupled-cluster model CC2. This work presents both the first comprehensive study of the two-photon absorption spectrum of YFP and the largest-scale coupled-cluster calculation of two-photon absorption that has ever been performed. We analyze the intermolecular charge-transfer (ICT) transitions in this stacked system and show that the ICT transitions are an important mechanism for enhancing the TPA cross sections in YFP. We investigate the distance dependence of the ICT transitions and show that their TPA cross sections are strongly dependent on the separation of the aromatic moieties. This provides a means for tuning the TPA properties of YFP and other structurally related fluorescent proteins through molecular engineering.

Rotational averaging of multiphoton absorption cross sections

Rotational averaging of tensors is a crucial step in the calculation of molecular properties in isotropic media. We present a scheme for the rotational averaging of multiphoton absorption cross sections. We extend existing literature on rotational averaging to even-rank tensors of arbitrary order and derive equations that require only the number of photons as input. In particular, we derive the first explicit expressions for the rotational average of five-, six-, and seven-photon absorption cross sections. This work is one of the required steps in making the calculation of these higher-order absorption properties possible. The results can be applied to any even-rank tensor provided linearly polarized light is used.

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Mo̸ller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input-output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C(60) fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.

Analytic Molecular Hessian Calculations for CC2 and MP2 Combined with the Resolution of Identity Approximation

An implementation of analytic second derivatives for the approximate coupled cluster singles and doubles model CC2 and for second-order Møller-Plesset perturbation theory (MP2) will be presented. The RI approximation for the two-electron repulsion integrals is used to reduce memory demands, operation count, and I/O requirements. During the calculation, the storage of [Formula: see text] quantities (where [Formula: see text] is a measure for the system size) can completely be avoided. It is shown that with the MP2 method and an appropriate scaling of the harmonic frequencies, especially C-F stretch frequencies are reproduced much better in comparison to experiments than with the B3LYP density functional. Similar advantages are observed for molecules with strong, internal van der Waals interactions. Spin scaling offers additional improvements in these cases. The implementation has been tested for molecules with up to 81 atoms and 684 basis functions.

Five-Photon Absorption and Selective Enhancement of Multiphoton Absorption Processes

We study one-, two-, three-, four-, and five-photon absorption of three centrosymmetric molecules using density functional theory. These calculations are the first ab initio calculations of five-photon absorption. Even- and odd-order absorption processes show different trends in the absorption cross sections. The behavior of all even- and odd-photon absorption properties shows a semiquantitative similarity, which can be explained using few-state models. This analysis shows that odd-photon absorption processes are largely determined by the one-photon absorption strength, whereas all even-photon absorption strengths are largely dominated by the two-photon absorption strength, in both cases modulated by powers of the polarizability of the final excited state. We demonstrate how to selectively enhance a specific multiphoton absorption process.

Excited state polarizabilities for CC2 using the resolution-of-the-identity approximation

We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D∞). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data.

Vibrational frequency scaling factors for correlation consistent basis sets and the methods CC2 and MP2 and their spin-scaled SCS and SOS variants

We present scaling factors for vibrational frequencies calculated within the harmonic approximation and the correlated wave-function methods coupled cluster singles and doubles model (CC2) and Møller-Plesset perturbation theory (MP2) with and without a spin-component scaling (SCS or spin-opposite scaling (SOS)). Frequency scaling factors and the remaining deviations from the reference data are evaluated for several non-augmented basis sets of the cc-pVXZ family of generally contracted correlation-consistent basis sets as well as for the segmented contracted TZVPP basis. We find that the SCS and SOS variants of CC2 and MP2 lead to a slightly better accuracy for the scaled vibrational frequencies. The determined frequency scaling factors can also be used for vibrational frequencies calculated for excited states through response theory with CC2 and the algebraic diagrammatic construction through second order and their spin-component scaled variants.

The impact of interplay between electronic and steric effects on the synthesis and the linear and non-linear optical properties of diketopyrrolopyrrole bearing benzofuran moieties

An in-depth investigation of the reaction of substituted salicylaldehydes with chloroacetonitrile led to the development of new conditions for the synthesis of 2-cyanobenzofurans. The crucial improvement lies in the use of phase-transfer catalysis in the second step, i.e., intramolecular aldol type condensation. In a two-step process, the reactants were transformed into a library of 3,6-bis(benzofuran-2-yl)diketopyrrolopyrroles. We show that the presence of a methyl group in a position adjacent to the cyano functionality only slightly decreased the yield of diketopyrrolopyrroles (to 30–57%). An analysis of the relationship between the degree of polarization/planarization of aryl-diketopyrrolopyrroles and their one- and two-photon spectroscopic properties is reported. Careful design of the desired dyes and enhanced control of their ability to assume a planar molecular structure resulted in interesting photophysical properties, such as absorption and emission in the so-called biological window. Despite having less promising linear spectroscopic properties, the deplanarized molecules possess pretty strong two-photon absorbing properties. Placing methyl groups at adjacent positions to the linkage between benzofuran and the DPP core caused the formation of yellow-emitting dyes with almost quantitative fluorescence quantum yield, moderate Stokes shift and reasonable two-photon absorption cross-sections.

Open-ended recursive calculation of single residues of response functions for perturbation-dependent basis sets.

We present theory, implementation, and applications of a recursive scheme for the calculation of single residues of response functions that can treat perturbations that affect the basis set. This scheme enables the calculation of nonlinear light absorption properties to arbitrary order for other perturbations than an electric field. We apply this scheme for the first treatment of two-photon circular dichroism (TPCD) using London orbitals at the Hartree-Fock level of theory. In general, TPCD calculations suffer from the problem of origin dependence, which has so far been solved by using the velocity gauge for the electric dipole operator. This work now enables comparison of results from London orbital and velocity gauge based TPCD calculations. We find that the results from the two approaches both exhibit strong basis set dependence but that they are very similar with respect to their basis set convergence.