Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory

Benchmarking two-photon absorption cross sections: performance of CC2 and CAM-B3LYP

We investigate the performance of CC2 and TDDFT/CAM-B3LYP for the calculation of two-photon absorption (TPA) strengths and cross sections and contrast our results to a recent coupled cluster equation-of-motion (EOM-EE-CCSD) benchmark study [K. D. Nanda and A. I. Krylov, J. Chem. Phys., 2015, 142, 064118]. In particular, we investigate whether CC2 TPA strengths are significantly overestimated compared to higher-level coupled-cluster calculations for fluorescent protein chromophores. Our conclusion is that CC2 TPA strengths are only slightly overestimated compared to the reference EOM-EE-CCSD results and that previously published overestimated cross sections are a result of inconsistencies in the conversion of the TPA strengths to macroscopic units. TDDFT/CAM-B3LYP TPA strengths, on the other hand, are found to be 1.5 to 3 times smaller than the coupled-cluster reference for the molecular systems considered. The unsatisfactory performance of TDDFT/CAM-B3LYP can be linked to an underestimation of excited-state dipole moments predicted by TDDFT/CAM-B3LYP.

Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks

The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.

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.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

DFT assessment of the spectroscopic constants and absorption spectra of neutral and charged diatomic species of group 11 and 14 elements

The spectroscopic constants and absorption spectra of neutral and charged diatomic molecules of group 11 and 14 elements formulated as [M(2)](+/0/-) (M = Cu, Ag, Au), and [E(2)](+/0/-) (E = C, Si, Ge, Sn, Pb) have been calculated at the PBE0/Def2-QZVPP level of theory. The electronic and bonding properties of the diatomics have been analyzed by natural bond orbital analysis approach and topology analysis by the atoms in molecules method. Particular emphasis was given on the absorption spectra of the diatomic species, which were simulated by time-dependent density functional theory calculations employing the hybrid Coulomb-attenuating CAM-B3LYP density functional. The simulated absorption spectra of the [M(2)](+/0/-) (M = Cu, Ag, Au) and [E(2)](+/0/-) (E = C, Si, Ge, Sn, Pb) species are in close resemblance with the experimentally observed spectra whenever available. The neutral M(2) and E(2) diatomics strongly absorb in the ultraviolet region, given rise to UVC, UVA and in a few cases UVB absorptions. In a few cases, weak absorbion bands also occur in the visible region. The absorption bands have thoroughly been analyzed and assignments of the contributing principal electronic transitions associated to individual excitations have been made.

Two-Photon Absorption in Fluorescent Protein Chromophores: TDDFT and CC2 Results

Two-photon spectroscopy of fluorescent proteins is a powerful bioimaging tool. Considerable effort has been made to measure absolute two-photon absorption (TPA) for the available fluorescent proteins. Being a technically involved procedure, there is significant variation in the published experimental measurements even for the same protein. In this work, we present a time-dependent density functional theory (TDDFT) study on isolated chromophores comparing the ability of four functionals (PBE0, B3LYP, CAM-B3LYP, and LC-BLYP) combined with the 6-31+G(d,p) basis set to reproduce averaged experimental TPA energies and cross sections. The TDDFT energies and TPA cross sections are also compared to corresponding CC2/6-31+G(d,p) results for excitation to S1 for the five smallest chromophores. In general, the computed TPA energies are less functional dependent than the TPA cross sections. The variation between functionals is more pronounced when higher-energy transitions are studied. Changes to the conformation of a chromophore are shown to change the TPA cross-section considerably. This adds to the difficulty of comparing an isolated chromophore to the one embedded in the protein environment. All functionals considered give moderate agreement with the corresponding CC2 results; in general, the TPA cross sections determined by TDDFT are 1.5-10 times smaller than the corresponding CC2 values for excitation to S1. LC-BLYP and CAM-B3LYP give erroneously large TPA cross sections in the higher-energy regions. On the other hand, B3LYP and PBE0 yield values that are of the same order of magnitude and in some cases very close to the averaged experimental data. Thus, based on the results reported here, B3LYP and PBE0 are the preferred functionals for screening chromphores for TPA. However, at best, TDDFT can be used to semiquantitatively scan chromophores for potential TPA probes and highlight spectroscopic peaks that could be present in the mature protein.

On the origin of the very strong two-photon activity of squaraine dyes – a standard/damped response theory study

In the present work, we report the mechanism of a very large increase in the two-photon (TP) activity of squaraine based molecules upon changing the substituents.

A density functional theory study of magneto-electric Jones birefringence of noble gases, furan homologues, and mono-substituted benzenes

We report on the results of a systematic ab initio study of the Jones birefringence of noble gases, of furan homologues, and of monosubstituted benzenes, in the gas phase, with the aim of analyzing the behavior and the trends within a list of systems of varying size and complexity, and of identifying candidates for a combined experimental/theoretical study of the effect. We resort here to analytic linear and nonlinear response functions in the framework of time-dependent density functional theory. A correlation is made between the observable (the Jones constant) and the atomic radius for noble gases, or the permanent electric dipole and a structure/chemical reactivity descriptor as the para Hammett constant for substituted benzenes.

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.

Solvent induced channel interference in the two-photon absorption process--a theoretical study with a generalized few-state-model in three dimensions

For the first time, we report the effect of interference between different optical channels on the two-photon absorption (TPA) process in three dimensions. We have employed response theory as well as a sum-over-states (SOS) approach involving few intermediate states to calculate the TPA parameters like transition probabilities (δ(TP)) and TPA tensor elements. In order to use the limited SOS approach, we have derived a new formula for a generalized few-state-model (GFSM) in three dimensions. Due to the presence of additional terms related to the angle between different transition moment vectors, the channel interference associated with the TPA process in 3D is significantly different and much more complicated than that in 1D and 2D cases. The entire study has been carried out on the two simplest Reichardt's dyes, namely 2- and 4-(pyridinium-1-yl)-phenolate (ortho- and para-betain) in gas phase, THF, CH(3)CN and water solvents. We have meticulously inspected the effect of the additional angle related terms on the overall TPA transition probabilities of the two 3D isomeric molecules studied and found that the interfering terms involved in the δ(TP) expression contribute both constructively and destructively as well to the overall δ(TP) value. Moreover, the interfering term has a more conspicuous role in determining the net δ(TP) associated with charge transfer transition in comparison to that of π-π* transition of the studied systems. Interestingly, our model calculations suggest that, for o- and p-betain, the quenching of destructive interference associated with a particular two-photon process can be done with high polarity solvents while the enhancement of constructive interference will be achieved in solvents having relatively small polarity. All the one- and two-photon parameters are evaluated using a range separated CAMB3LYP functional.

Two-photon polarization dependent spectroscopy in chirality: a novel experimental-theoretical approach to study optically active systems

Many phenomena, including life itself and its biochemical foundations are fundamentally rooted in chirality. Combinatorial methodologies for catalyst discovery and optimization remain an invaluable tool for gaining access to enantiomerically pure compounds in the development of pharmaceuticals, agrochemicals, and flavors. Some exotic metamaterials exhibiting negative refractive index at optical frequencies are based on chiral structures. Chiroptical activity is commonly quantified in terms of circular dichroism (CD) and optical rotatory dispersion (ORD). However, the linear nature of these effects limits their application in the far and near-UV region in highly absorbing and scattering biological systems. In order to surmount this barrier, in recent years we made important advancements on a novel non linear, low-scatter, long-wavelength CD approach called two-photon absorption circular dichroism (TPACD). Herein we present a descriptive analysis of the optics principles behind the experimental measurement of TPACD, i.e., the double L-scan technique, and its significance using pulsed lasers. We also make an instructive examination and discuss the reliability of our theoretical-computational approach, which uses modern analytical response theory, within a Time-Dependent Density Functional Theory (TD-DFT) approach. In order to illustrate the potential of this novel spectroscopic tool, we first present the experimental and theoretical results obtained in C(2)-symmetric, axially chiral R-(+)-1,1'-bi(2-naphthol), R-BINOL, a molecule studied at the beginning of our investigation in this field. Next, we reveal some preliminary results obtained for (R)-3,3'-diphenyl-2,2'-bi-1-naphthol, R-VANOL, and (R)-2,2'-diphenyl-3,3'-(4-biphenanthrol), R-VAPOL. This family of optically active compounds has been proven to be a suitable model for the structure-property relationship study of TPACD, because its members are highly conjugated yet photo-stable, and easily derivatized at the 5- and 6-positions. With the publication of these outcomes we hope to motivate more members of the scientist community to engage in state-of-the-art TPACD spectroscopy.