Beyond the Förster formulation for resonance energy transfer: the role of dark states

Resonance Energy Transfer (RET) is investigated in pairs of charge-transfer (CT) chromophores. CT chromophores are an interesting class of π conjugated chromophores decorated with one or more electron-donor and acceptor groups in polar (D-π-A), quadrupolar (D-π-A-π-D or A-π-D-π-A) or octupolar (D(-π-A)(3) or A(-π-D)(3)) structures. Essential-state models accurately describe low-energy linear and nonlinear spectra of CT-chromophores and proved very useful to describe spectroscopic effects of electrostatic interchromophore interactions in multichromophoric assemblies. Here we apply the same approach to describe RET between CT-chromophores. The results are quantitatively validated by an extensive comparison with time-dependent density functional theory (TDDFT) calculations, confirming that essential-state models offer a simple and reliable approach for the calculation of electrostatic interchromophore interactions. This is an important result since it sets the basis for more refined treatments of RET: essential-state models are in fact easily extended to account for molecular vibrations in truly non-adiabatic approaches and to account for inhomogeneous broadening effects due to polar solvation. Optically forbidden (dark) states of quadrupolar and octupolar chromophores offer an interesting opportunity to verify the reliability of the dipolar approximation. In striking contrast with the dipolar approximation that strictly forbids RET towards or from dark states, our results demonstrate that dark states can take an active role in RET with interaction energies that, depending on the relative orientation of the chromophores, can be even larger than those relevant to allowed states. Essential-state models, whose predictions are quantitatively confirmed by TDDFT results, allow us to relate RET interaction energies towards allowed and dark states to the supramolecular symmetry of the RET-pair, offering reliable design strategies to optimize RET-interactions.     

Second harmonic generation from small gold metallic particles: from the dipolar to the quadrupolar response

Hyper Raleigh scattering, a common technique to investigate the second harmonic light scattered from a liquid suspension of molecular compounds and to determine their quadratic hyperpolarizability, has been used for aqueous suspensions of gold nanoparticles, the diameter of which ranges from 20 up to 150 nm. The hyper Rayleigh signal intensity was recorded as a function of the angle of polarization of the incident fundamental wave. For the particles with a diameter smaller than 50 nm, the response is dominated by the dipolar contribution arising from the deviation of the particle shape from that of a perfect sphere. For larger diameter particles, retardation effects in the interaction of the electromagnetic fields with the particles cannot be neglected any longer and the response deviates from the pure dipolar response, exhibiting a strong quadrupolar contribution. It is then shown that in order to quantify the relative magnitude of these two dipolar and quadrupolar contributions, a weighting parameter zeta(V) which equals unity for a pure quadrupolar contribution and vanishes for a pure dipolar response, can be introduced.     

Consideration of dipole–quadrupole interactions in molecular based equations of state

The thermodynamic behaviour of a number of real substances is determined by dipolar as well as quadrupolar interactions of the molecules. In equations of state (EOS) like, e.g. BACKONE separate contributions to the Helmholtz energy for the dipolar and the quadrupolar interactions are considered but no cross contributions. Here, the concept of effective dipole and quadrupole contributions is suggested in which the effective dipole strength μ_e is influenced by the quadrupole cross interaction. Similarily, the effective quadrupole strength Q_e takes into account the dipole cross interaction. In order to arrive at these effective dipolar and quadrupolar strengths, molecular simulations are performed. From the simulation results correlation equations are derived which are used in combination with BACKONE for the calculation of vapour–liquid equilibria (VLE) of real mixtures. By using these effective moments, the only required binary mixing rule parameter k_ij tends to small values of about 0.01 and becomes temperature-independent. Moreover, the VLE pressures are predicted now considerably better than without consideration of the cross contributions.     

Density functional response theory calculations of three-photon absorption

Three-photon absorption probabilities delta(3PA) have been calculated through application of a recently derived method for cubic response functions within density functional theory (DFT). Calculations are compared with Hartree-Fock (HF) and with a coupled cluster hierarchy of models in a benchmarking procedure. Except for cases having intermediate states near resonance, density functional theory is demonstrated to be in sufficient agreement with the highly correlated methods in order to qualify for predictions of delta(3PA). For the larger systems addressed, a set of acceptor A and donor D substituted pi-conjugated systems formed by trans-stilbene and dithienothiophene (DTT), we find noticeable differences in the magnitude of delta(3PA) between HF and DFT, although similar trends are followed. It is shown that the dipolar structures, TS-AD and DTT-AD, have substantially larger delta(3PA) than other types of modifications which is in accordance with observations for two-photon absorption. This is the first application of density functional theory to three-photon absorption beyond the use of few-state models.     

Experimental studies of light-induced charge transfer and charge redistribution in (X(2)-bipyridine)Re(I)(CO)(3)Cl complexes

Stark emission spectroscopy, transient DC photoconductivity (TDCP), and ground-state dipole moment measurements have been used to evaluate charge transfer (CT) within various (X(2)-bipyridine)Re(I)(CO)(3)Cl complexes following (3)MLCT excited-state formation. The Stark technique reports on vector differences between ground-state (mu(g)) and excited-state (mu(e)) dipole moments, while TDCP, when combined with independently obtained mu(g) information, reports on scalar differences. For systems featuring collinear, same-signed ground- and excited-state dipole moments, the scalar and vector differences are equivalent. However, for the low symmetry systems studied here, they are distinctly different. The vector difference yields the effective adiabatic one-electron-transfer distance (R(12)), while the combined vector and scalar data yield information about dipole rotation upon ground-state/excited-state interconversion. For the systems examined, charge transfer distances are substantially smaller than geometric electron-donor/electron-acceptor site separation distances. The measured distances are significantly affected by changes in acceptor ligand substituent composition. Electron-donating substituents decrease CT distances, while electron-withdrawing substituents increase CT distances, as do aromatic substituents that are capable of expanding the bipyridyl ligand (acceptor ligand) pi system. The Stark measurements additionally indicate that the CT vector and the transition dipole moment are significantly orthogonal, a consequence of strong polarization of the Re-Cl bond (orthogonal to the metal/acceptor-ligand plane) in the ground electronic state and relaxation of the polarization in the upper state. The ground-state Re-Cl bond polarization is sufficiently large that the overall ground-state scalar dipole moment exceeds the overall excited-state scalar dipole moment, despite transfer of an electron from the metal center to the diimine ligand. This finding provides an explanation for the otherwise puzzling negative solvatochromism exhibited in this family of compounds. Combining TDCP and Stark results, we find that the dipole moment can be rotated in some instances by more than 90 degrees upon (3)MLCT excited-state formation. The degree of rotation or reorientation can be modulated by changing the identity of the acceptor ligand substituents. Reorientational effects are smallest when the compounds feature aromatic substituents capable of spatially extending the pi system of the acceptor ligand.     

Solid‐state NMR Spectroscopy of Quadrupolar Nuclei in Inorganic Chemistry

We here review the principles and applications of solid‐state NMR spectroscopy of quadrupolar nuclei, with a special emphasis on structural studies of inorganic solids. Most NMR‐observable nuclei have spin I > 1/2, and possess a quadrupole moment. The resulting quadrupolar interaction severely broadens the resonances, but also encapsulates valuable information about the symmetry of the electronic surroundings of the observed nucleus. The effect of the quadrupolar interaction, as well as that of the chemical shift and dipolar interaction, on solid‐state NMR spectra is examined in this article. To regain good resolution, specifically designed NMR techniques exist to remove the quadrupolar broadening, i.e. overtone and MQMAS spectroscopy, the principles of which are outlined here. In addition, the possibility of distance measurements via the dipolar interaction using the REDOR technique is discussed. The combined information derived from distance measurements, quadrupolar and chemical shift parameters can be helpful for determination of the crystal structure, or for detection of impurity phases, as illustrated by surveying a number of case studies covering spin I = 1, 3/2, 5/2 and 7/2.     

Limits in Proton Nuclear Singlet‐State Lifetimes Measured with para‐Hydrogen‐Induced Polarization

The synthesis of a hyperpolarized molecule was developed, where the polarization and the singlet state were preserved over two controlled chemical steps. Nuclear singlet‐state lifetimes close to 6 min for protons are reported in dimethyl fumarate. Owing to the high symmetry (AA′X₃X₃′ and A₂ systems), the singlet‐state readout requires either a chemical desymmetrization or a long and repeated spin lock. Using DFT calculations and relaxation models, we further determine nuclear spin singlet lifetime limiting factors, which include the intramolecular dipolar coupling mechanism (proton–proton and proton–deuterium), the chemical shift anisotropy mechanism (symmetric and antisymmetric), and the intermolecular dipolar coupling mechanism (to oxygen and deuterium). If the limit of paramagnetic relaxation caused by residual oxygen could be lifted, the intramolecular dipolar coupling to deuterium would become the limiting relaxation mechanism and proton lifetimes upwards of 26 min could become available in the molecules considered here (dimethyl maleate and dimethyl fumarate).     

Two-photon absorption in quadrupolar pi-conjugated molecules: influence of the nature of the conjugated bridge and the donor-acceptor separation

Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems.     

Electronic energy transfer between metastable argon atoms and ground-state oxygen atoms

The transfer of electronic energy between metastable argon and ground-state oxygen atoms has been studied in a discharge-flow apparatus. The excitation energy of the argon metastables is transferred to the 3p ³P state of atomic oxygen with a cross section of 3 A². The energy transfer is discussed in terms of an ionic-intermediate, curve-crossing mechanism for which the calculated cross section is 13 A².     

Efficient Excited‐State Symmetry Breaking in a Cationic Quadrupolar System Bearing Diphenylamino Donors

We report a joint experimental and theoretical investigation of a quadrupolar D–π–A⁺–π–D system, the electron donors being diphenylamino groups and the electron acceptor being a methylpyridinium, in comparison with the dipolar D–π–A⁺ system. The emission spectra of the two compounds overlap in all the investigated solvents. This finding could be rationalized by TD‐DFT calculations: the LUMO–HOMO molecular orbitals involved in the emission transition are localized on the same branch of the quadrupolar structure that becomes the fluorescent portion, corresponding to that of the single‐arm compound. Excited‐state symmetry breaking has been rarely observed for quadrupolar systems showing negative solvatochromism and is here surprisingly revealed, even in low polarity solvents. Femtosecond transient absorption measurements revealed that an efficient photoinduced intramolecular charge transfer takes place in the quadrupolar chromophore, more efficient than in its dipolar analogue. This result is promising in view of the application of these compounds as novel two‐photon absorbing materials.     

Electric polarization effects on the electronic spectral shift of centrosymmetric compounds

The classic dielectric dipolar Onsager model was extended to include quadrupolar interactions between solute molecules and solvents with different polarities. A multiparametric solvatochromic expression, based on the point quadrupole moment inside a spherical cavity embedded in a dielectric continuum, is applied to centrosymmetric sulfonamide porphyrins, zinc tetraphenyl porphyrin, squaraine and 9,10-dicyanoanthracene, in order to account for the quadrupolar polarization effect of solute molecules. The reaction field polarity functions created respectively by dipole and quadrupole moments are compared and found to be linearly correlated.     

Critical electron binding to linear electric quadrupole systems

Results for critical quadrupolar moments for electron binding to fixed, point-charge systems are normalized, extended, and displayed in graphical forms. The influence of rotational degrees of freedom on critical binding to quadrupolar systems is examined through calculations of critical moments for electron binding to linear electric quadrupolar rotors. The results are presented for rotors covering useful ranges of size and inertial parameters. The effect of rotational degrees of freedom on critical binding is found to be less important for quadrupolar as compared to dipolar rotors.     

Two-photon absorption at telecommunications wavelengths in a dipolar chromophore with a pyrrole auxiliary donor and thiazole auxiliary acceptor

Three new dipolar chromophores based on a diaklyaminophenyl donor, a pyrrole auxiliary donor, a thiazole auxiliary acceptor, and strong heterocyclic acceptors have been synthesized. For one of these compounds we have measured a very large non-degenerate two-photon cross section of ca. 1500 GM in the near-IR telecommunications range using a pump-probe technique. Calculations indicate the cross section for degenerate two-photon absorption is likely to be ca. 60% of this value.     

14N Solid‐State NMR Spectroscopy of Amino Acids

¹⁴N ultra‐wideline solid‐state NMR (SSNMR) spectra were obtained for 16 naturally occurring amino acids and four related derivatives by using the WURST–CPMG (wideband, uniform rate, and smooth truncation Carr–Purcell–Meiboom–Gill) pulse sequence and frequency‐stepped techniques. The ¹⁴N quadrupolar parameters were measured for the sp³ nitrogen moieties (quadrupolar coupling constant, C_Q, values ranged from 0.8 to 1.5 MHz). With the aid of plane‐wave DFT calculations of the ¹⁴N electric‐field gradient tensor parameters and orientations, the moieties were grouped into three categories according to the values of the quadrupolar asymmetry parameter, η_Q: low (≤0.3), intermediate (0.31–0.7), and high (≥0.71). For RNH₃⁺ moieties, greater variation in N?H bond lengths was observed for systems with intermediate η_Q values than for those with low η_Q values (this variation arose from different intermolecular hydrogen‐bonding arrangements). Strategies for increasing the efficiency of ¹⁴N SSNMR spectroscopy experiments were discussed, including the use of sample deuteration, high‐power ¹H decoupling, processing strategies, high magnetic fields, and broadband cross‐polarization (BRAIN‐CP). The temperature‐dependent rotations of the NH₃ groups and their influence on ¹⁴N transverse relaxation rates were examined. Finally, ¹⁴N SSNMR spectroscopy was used to differentiate two polymorphs of l ‐histidine through their quadrupolar parameters and transverse relaxation time constants. The strategies outlined herein permitted the rapid acquisition of directly detected ¹⁴N SSNMR spectra that to date was not matched by other proposed methods.     

Macroscopic order and electro-optic response of dipolar chromophore-polymer materials.

This Minireview considers the key factors that govern the organization of macroscopic polarization in nonlinear optical systems obtained by electric poling of organic dipolar chromophores dissolved in polymer matrices. The macroscopic electric polarization depends on the thermodynamic state of the dipole system. The dependence of the paraelectric and antiferroelectric states of dipolar chromophores on the chromophore concentration and the strength of the poling field is discussed. Phase transitions between the para- and antiferroelectric states are investigated within the limits of the Ising and isotropic models for the chromophore dipoles and are considered for varying chromophore concentration, poling field strength, and macroscopic shape of the sample used for poling. The macroscopic polarization and electro-optic coefficient of the material change drastically upon phase transition. The theories are compared with the experimental data on the electro-optic coefficient dependence on the chromophore concentration. The isotropic dipole model shows excellent agreement with experiment for the chromophore systems most commonly used in nonlinear optics.     

Linearity and quadrupolarity of tetragonal and cylindrical penning traps of arbitrary length-to-width ratio

The two most popular Penning traps in use for Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry are tetragonal (i. e., orthorhombic with square cross section) and cylindrical. Here we compare tetragonal and cylindrical traps as a function of aspect (length-to-width) ratio and position within the trap, by comparing the numerically computed (from Simion 6.0) electric potential field of a given trap relative to each of three idealized potentials required for FT-ICR experiments: dipolar one-dimensional potential for alternating current (ac) excitation/detection of cyclotron motion, azimuthal two-dimensional quadrupolar potential for ac excitation for ion axialization, and axial three-dimensional quadrupolar potential for direct current axial confinement of ions. Our numerically computed results agree well with those previously derived analytically. The numerical approach provides a simpler and more accessible means for analyzing the aforementioned potentials. Moreover, the numerical approach (unlike the analytical approach) readily extends to traps of lower symmetry. Finally, even when analytical solutions are available, the numerical method presented here is complementary, since it provides a useful check on the validity of the derived equations.     

Q.E.COSY: determining sign and size of small deuterium residual quadrupolar couplings using an extended E.COSY principle

Residual quadrupolar couplings contain important structural information comparable with residual dipolar couplings. However, the measurement of sign and size of especially small residual quadrupolar couplings is difficult. Here, we present an extension of the E.COSY principle to spin systems consisting of a Spin 1 coupled to a spin ½ nucleus, which allows the determination of the sign of the quadrupolar coupling of the Spin 1 nucleus relative to the heteronuclear coupling between the spins. The so‐called Q.E.COSY approach is demonstrated with its sign‐sensitivity using variable angle NMR, stretched gels and liquid crystalline phases applied to various CD and CD₃ groups. Especially the sign‐sensitive measurement of residual quadrupolar couplings that remain unresolved in conventional deuterium 1D spectra is shown. Copyright © 2016 John Wiley & Sons, Ltd.