Second-harmonic generation of solvated molecules using multiconfigurational self-consistent-field quadratic response theory and the polarizable continuum model

Exceptional three- to six-photon absorption at organometallic dendrimers

The light-intensity dependence of multi-photon absorption (MPA) affords outstanding spatial control. Furthermore, compared to the higher-energy photons needed for analogous linear absorption, the lower-energy photons involved in MPA often correspond to important wavelengths, such as those of the biological and telecommunications "windows". It is therefore of crucial importance to develop molecules that exhibit outstanding MPA cross-sections. However, although progress has been made with two-photon absorption, there is currently a dearth of efficient instantaneous n-photon absorbers (n > 2), a key reason being the scarcity of structure-property studies required to understand higher-order MPA. We herein report systematically-varied metallodendrimers up to third-generation in size, together with their nonlinear absorptive responses over the spectral range 600-2520 nm. We show that the dendrimers exhibit exceptional instantaneous three- to six-photon absorption cross-sections, with maximal values increasing with dendrimer generation and installation of solubilizing group, and we report that changing the groups at the dendrimer periphery can shift the wavelengths of the nPA maxima. We also describe time-dependent DFT studies that have facilitated assignment of the key linear and nonlinear transitions and disclosed the crucial role of the metal in the outstanding MPA performance.

E/Z Molecular Photoswitches Activated by Two-Photon Absorption: Comparison between Different Families

Nonlinear optical techniques as two-photon absorption (TPA) have raised relevant interest within the last years due to the capability to excite chromophores with photons of wavelength equal to only half of the corresponding one-photon absorption energy. At the same time, its probability being proportional to the square of the light source intensity, it allows a better spatial control of the light-induced phenomenon. Although a consistent number of experimental studies focus on increasing the TPA cross section, very few of them are devoted to the study of photochemical phenomena induced by TPA. Here, we show a design strategy to find suitable E/Z photoswitches that can be activated by TPA. A theoretical approach is followed to predict the TPA cross sections related to different excited states of various photoswitches’ families, finally concluding that protonated Schiff-bases (retinal)-like photoswitches outperform compared to the others. The donor-acceptor substitution effect is therefore rationalized for the successful TPA activatable photoswitch, in order to maximize its properties, finally also forecasting a possible application in optogenetics. Some experimental measurements are also carried out to support our conclusions.

Nuclear spin-induced optical rotation of functional groups in hydrocarbons

Nuclear spin-induced optical rotation (NSOR) is a nuclear magneto-optic effect manifesting as a rotation of the plane of polarization of linearly polarized light induced by nuclear magnetic moments within a molecule. NSOR probes molecular optical properties through localized nuclear interactions and has potential to be developed into a new spectroscopic tool. However, so far the connection between the molecular structure and NSOR response has not been systematically investigated. To obtain insight into this relation and to assess its viability as a foundation for a new spectroscopic method, NSOR of 1H and 13C nuclei in a set of hydrocarbon molecules with various structural motifs is theoretically investigated using density functional theory calculations. The results reveal that NSOR intensities are correlated with several structural features of the molecules, such as the position of the nucleus in the carbon chain, isomerism and presence of nearby unsaturated groups. Specific patterns connecting NSOR to the local chemical environment of the nucleus can be observed. It is also shown that this effect can be to a good approximation modelled as a sum of individual contributions from nearby chemical groups, allowing for a rapid estimation of its values. The demonstrated systematic dependence of the NSOR signal on the molecular structure is a desirable feature for theoretical and experimental development of new spectroscopic methods based on this phenomenon.

A generalized few-state model for the first hyperpolarizability

The properties of molecules depend on their chemical structure, and thus, structure-property relations help design molecules with desired properties. Few-state models are often used to interpret experimental observations of non-linear optical properties. Not only the magnitude but also the relative orientation of the transition dipole moment vectors is needed for few-state models of the non-linear optical properties. The effect of the relative orientation of the transition dipole moment vectors is called dipole alignment, and this effect has previously been studied for multiphoton absorption properties. However, so far, no such studies are reported for the first hyperpolarizability. Here, we present a generalized few-state model for the static and dynamic first hyperpolarizability β, accounting for the effect of dipole alignment. The formulas derived in this work are general in the sense that they can be used for any few-state model, i.e., a two-state model, a three-state model, or, in general, an n-state model. Based on the formulas, we formulate minimization and maximization criteria for the alignment of transition dipole moment vectors. We demonstrate the importance of dipole alignment by applying the formulas to the static first hyperpolarizability of ortho-, meta-, and para-nitroaniline. The formulas and the analysis provide new ways to understand the structure-property relationship for β and can hence be used to fine-tune the magnitude of β in a molecule.

Open-ended formulation of self-consistent field response theory with the polarizable continuum model for solvation

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Interplay of twist angle and solvents with two-photon optical channel interference in aryl-substituted BODIPY dyes

Channel interference plays a crucial role in understanding the physics behind multiphoton absorption processes. In this work, we study the role of channel interference and solvent effects on the two-photon absorption in aryl-substituted boron dipyrromethene (BODIPY) dyes, a class of intramolecular charge-transfer (ICT) molecules. For this purpose, we consider fourteen dyes of this class with various donor/acceptor substitutions at the para position of the phenyl ring and with or without methyl (-CH₃) substitution on the BODIPY moiety. The presence of a methyl group on the BODIPY moiety affects the dihedral angle significantly, which in turn affects the one- (OPA) and two-photon absorption (TPA) properties of the molecules. Among the molecules studied, the one having the strong electron-donating dimethylamino group and no methyl substitution at the BODIPY moiety is found to have the highest TPA cross section. Our few-state model analysis shows that the large TPA activity of this molecule is due to the all positive contributions from different channel interference terms. Change in dielectric constant of the medium is found to have a profound impact on both the magnitude and sign of the channel interference terms. The magnitude of destructive channel interference gradually decreases with decreasing solvent polarity and becomes constructive in a low-polarity solvent. We also study the effect of rotating the phenyl ring with respect to the BODIPY moiety on the TPA activity. In the gas phase and in different solvents, we found that channel interference is changed from destructive to constructive on twisting the molecule. These results are explained by considering different dipole-, energy- and angle-terms appearing in the expression of a two-state model.

Optical absorption and magnetic circular dichroism spectra of thiouracils: a quantum mechanical study in solution

The excited electronic states of thiouracils, the analogues of uracil where the carbonyl oxygens are substituted by sulphur atoms, have been investigated by computing the magnetic circular dichroism (MCD) and one-photon absorption (OPA) spectra at the TD-DFT level of theory.

Solvent effects on static polarizability, static first hyperpolarizability and one- and two-photon absorption properties of functionalized triply twisted Möbius annulenes: a DFT study

Solvent effects on the polarizability (α), static first hyperpolarizability (β) and one- and two-photon absorption (OPA and TPA) properties of triply twisted Möbius annulenes.

Photoinduced Charge Transport in a BHJ Solar Cell Controlled by an External Electric Field

This study investigated theoretical photoinduced charge transport in a bulk heterojunction (BHJ) solar cell controlled by an external electric field. Our method for visualizing charge difference density identified the excited state properties of photoinduced charge transfer, and the charge transfer excited states were distinguished from local excited states during electronic transitions. Furthermore, the calculated rates for the charge transfer revealed that the charge transfer was strongly influenced by the external electric field. The external electric field accelerated the rate of charge transfer by up to one order when charge recombination was significantly restrained. Our research demonstrated that photoinduced charge transport controlled by an external electric field in a BHJ solar cell is efficient, and the exciton dissociation is not the limiting factor in organic solar cells.Our research should aid in the rational design of a novel conjugated system of organic solar cells.

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Jones and magnetoelectric birefringence of pure substances — A computational study

We present the first investigation of condensed-phase effects on the Jones (and magnetoelectric) birefringence of a set of nondipolar (CCl4 and CS2) and dipolar (nitro- and chloro-benzene) molecules using a recent implementation of the polarizable continuum model for cubic response functions at the time-dependent density-functional level of theory. The condensed-phase calculations have been performed on the neat liquids of the sample molecules using a nonequilibrium solvation scheme to properly account for the solute–solvent interactions in the presence of a frequency-dependent electromagnetic field. It is demonstrated that the condensed-phase effects as modelled by the polarizable continuum model can be substantial, increasing the observable birefringence by more than sixty percent in the case of CCl4, and by a factor of more than three for CS2. Solvent effects are also substantial for the dipolar molecules, leading to an enhancement by a factor of roughly five for nitrobenzene and by a bit less than 30% for chlorobenzene. Comparison is made with the results of experiment. Our calculated anisotropies confirm that the effect is below current experimental detection limits for CCl4 and CS2. We compute Jones constants of the same order of magnitude as the upper limits given in experiment for nitro- and chlorobenzene.

Applicability of hybrid density functional theory methods to calculation of molecular hyperpolarizability

The donor/acceptor (D/A) substituted pi-conjugated organic molecules possess extremely fast nonlinear optical (NLO) response time that is purely electronic in origin. This makes them promising candidates for optoelectronic applications. In the present study, we utilized four hybrid density functionals (B3LYP, B97-2, PBE0, BMK), Hartree-Fock, and second order Moller-Plesset correlation energy correction, truncated at second-order (MP2) methods with different basis sets to estimate molecular first hyperpolarizability (beta) of D/A-substituted benzenes and stilbenes (D=OMe, OH, NMe(2), NH(2); A=NO(2), CN). The results of density functional theory (DFT) calculations are compared to those of MP2 method and to the experimental data. We addressed the following questions: (1) the accurate techniques to compare calculated results to each other and to experiment, (2) the choice of the basis set, (3) the effect of molecular planarity, and (4) the choice of the method. Comparison of the absolute values of hyperpolarizabilities obtained computationally and experimentally is complicated by the ambiguities in conventions and reference values used by different experimental groups. A much more tangible way is to compare the ratios of beta's for two (or more) given molecules of interest that were calculated at the same level of theory and measured at the same laboratory using the same conventions and reference values. Coincidentally, it is the relative hyperpolarizabilities rather than absolute ones that are of importance in the rational molecular design of effective NLO materials. This design includes prediction of the most promising candidates from particular homologous series, which are to be synthesized and used for further investigation. In order to accomplish this goal, semiquantitative level of accuracy is usually sufficient. Augmentation of the basis set with polarization and diffuse functions changes beta by 20%; however, further extension of the basis set does not have significant effect. Thus, we recommend 6-31+G(*) basis set. We also show that the use of planar geometry constraints for the molecules, which can somewhat deviate from planarity in the gas phase, leads to sufficient accuracy (with an error less than 10%) of predicted values. For all the molecules studied, MP2 values are in better agreement with experiment, while DFT hybrid methods overestimate beta values. BMK functional gives the best agreement with experiment, with systematic overestimation close to the factor of 1.4. We propose to use the scaled BMK results for prediction of molecular hyperpolarizability at semiquantitative level of accuracy.

Visualizations of transition dipoles, charge transfer, and electron-hole coherence on electronic state transitions between excited states for two-photon absorption

The one-photon absorption (OPA) properties of donor-pi-bridge-acceptor-pi-bridge-donor (D-pi-A-pi-D)-type 2,1,3-benzothiadiazoles (BTD) were studied with two dimensional (2D) site and three dimensional (3D) cube representations. The 2D site representation reveals the electron-hole coherence on electronic state transitions from the ground state. The 3D representation shows the orientation of transition dipole moment with transition density, and the charge redistribution on the excited states with charge difference density. In this paper, we further developed the 2D site and 3D cube representations to investigate the two-photon absorption (TPA) properties of D-pi-A-pi-D-type BTD on electronic transitions between excited states. With the new developed 2D site and 3D cube representations, the orientation of transition dipole moment, the charge redistribution, and the electron-hole coherence for TPA of D-pi-A-pi-D-type BTD on electronic state transitions between excited states were visualized, which promote deeper understanding to the optical and electronic properties for OPA and TPA.

Degenerate four-wave mixing in solution by cubic response theory and the polarizable continuum model

We have derived and implemented the solvent contribution to the cubic response function for the polarizable continuum model in its integral equation formulation. The present formulation is valid both at the Hartree-Fock and at the Kohn-Sham density functional levels of theory, because both bear the same formal description of the solvent contribution through an additional additive term in the Hamiltonian operator. This new implementation is used to compute the solvent effect for the degenerate four-wave mixing process on three different classes of heteroaromatic chromophores: (I) triazine, benzoxazole, benzimidazole, and benzothiazole; (II) three benzothiazole derivatives; and (III) three tri-s-triazine derivatives. The results are first discussed in terms of the solvent effects on the calculated property and then compared to experimental data for the substrates of class (I) and (II).

Combined density functional/polarizable continuum model study of magnetochiral birefringence: Can theory and experiment be brought to agreement?

The magnetic-field-induced axial birefringence (magnetochirality) of five closed-shell chiral molecules (three substituted oxiranes, carvone, and limonene) is studied at the density functional theory level using Becke's 3-parameter Lee-Yang-Parr functional and frequency-dependent quadratic response theory. The influence of the environment and the conformational distribution on the property is also studied. The environment effects are described by the polarizable continuum model in its integral-equation formulation. The effect of the conformational distribution is investigated by performing calculations on several conformers-for carvone and limonene-followed by Boltzmann averaging. The calculated values for the magnetochiral birefringence are compared to previous ab initio results and experimental data where available. The refined model presented here brings the ab initio values closer to experiment. Still, disagreements remain in some cases and it appears difficult to resolve these discrepancies.

Parallelization of the integral equation formulation of the polarizable continuum model for higher-order response functions

We present a parallel implementation of the integral equation formalism of the polarizable continuum model for Hartree-Fock and density functional theory calculations of energies and linear, quadratic, and cubic response functions. The contributions to the free energy of the solute due to the polarizable continuum have been implemented using a master-slave approach with load balancing to ensure good scalability also on parallel machines with a slow interconnect. We demonstrate the good scaling behavior of the code through calculations of Hartree-Fock energies and linear, quadratic, and cubic response function for a modest-sized sample molecule. We also explore the behavior of the parallelization of the integral equation formulation of the polarizable continuum model code when used in conjunction with a recent scheme for the storage of two-electron integrals in the memory of the different slaves in order to achieve superlinear scaling in the parallel calculations.

Evaluation of alternative sum-over-states expressions for the first hyperpolarizability of push-pull π-conjugated systems

A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (beta) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal beta of four typical push-pull pi-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for beta and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull pi-conjugated systems to estimate the static beta, and the error in the value so obtained, by averaging the Kuzyk and traditional results.

Acidoswitchable NLO-phores: Benzimidazolo[2,3-b]oxazolidines

This paper presents a series of acidoswitchable NLO-phores combining the 9-methylbenzimidazolo[2,3-b]oxazolidine core with various pi systems such as phenylethenyl, phenylethynyl, and naphthylethenyl. All the prepared derivatives are shown to display acidochromic behavior at ambient temperature. The remarkable contrast in the NLO response along the reversible transformations observed in HRS experiments is rationalized by high level theoretical calculations.