Dynamics Of Chromophore Research Articles

QM/MM Study of Substituent and Solvent Effects on the Excited State Dynamics of the Photoactive Yellow Protein Chromophore.

Substituent and solvent effects on the excited state dynamics of the Photoactive Yellow Protein chromophore are studied using the average solvent electrostatic potential from molecular dynamics (ASEP/MD) method. Four molecular models were considered: the ester and thioester derivatives of the p-coumaric acid anion and their methylated derivatives. We found that the solvent produces dramatic modifications on the free energy profile of the S1 state: 1) Two twisted structures that are minima in the gas phase could not be located in aqueous solution. 2) Conical intersections (CIs) associated with the rotation of the single bond adjacent to the phenyl group are found for the four derivatives in water solution but only for thio derivatives in the gas phase. 3) The relative stability of minima and CIs is reverted with respect to the gas phase values, affecting the prevalent de-excitation paths. As a consequence of these changes, three competitive de-excitation channels are open in aqueous solution: the fluorescence emission from a planar minimum on S1, the trans-cis photoisomerization through a CI that involves the rotation of the vinyl double bond, and the nonradiative, nonreactive, de-excitation through the CI associated with the rotation of the single bond adjacent to the phenyl group. In the gas phase, the minima are the structures with the lower energy, while in solution these are the conical intersections. In solution, the de-excitation prevalent path seems to be the photoisomerization for oxo compounds, while thio compounds return to the initial trans ground state without emission.

A metal-organic framework as a flask: photophysics of confined chromophores with a benzylidene imidazolinone core.

Photophysics and dynamics of chromophores with a benzylidene imidazolinone core, responsible for emission of green fluorescent protein variants, were studied as a function of host topology by three approaches. Coordinative, non-coordinative, and "fastened" immobilization were utilized to study chromophore emission. Variable-temperature quadrupolar spin-echo 2H NMR spectra are reported.

Electronic structure and dynamics of torsion-locked photoactive yellow protein chromophores.

The photocycle of photoactive yellow protein (PYP) begins with small-scale torsional motions of the chromophore leading to large-scale movements of the protein scaffold triggering a biological response. The role of single-bond torsional molecular motions of the chromophore in the initial steps of the PYP photocycle are not fully understood. Here, we employ anion photoelectron spectroscopy measurements and quantum chemistry calculations to investigate the electronic relaxation dynamics following photoexcitation of four model chromophores, para-coumaric acid, its methyl ester, and two analogues with aliphatic bridges hindering torsional motions around the single bonds adjacent to the alkene group. Following direct photoexcitation of S1 at 400 nm, we find that both single bond rotations play a role in steering the PYP chromophore through the S1/S0 conical intersection but that rotation around the single bond between the alkene moiety and the phenoxide group is particularly important. Following photoexcitation of higher lying electronic states in the range 346-310 nm, we find that rotation around the single bond between the alkene and phenoxide groups also plays a key role in the electronic relaxation from higher lying states to the S1 state. These results have potential applications in tuning the photoresponse of photoactive proteins and materials with chromophores based on PYP.

Charge-Induced Long-Range Order in a Room-Temperature Ionic Liquid.

We report direct evidence for charge-induced long-range (ca. 100 μm) order in the room-temperature ionic liquid (IL) 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM(+)BF4(-)), supported on a silica surface. We have measured the rotational diffusion dynamics of anionic, cationic, and neutral chromophores as a function of distance from a silica surface. The results reflect the excess charge density gradient induced in the IL by the (negative) charge present on the silica surface. Identical measurements in ethylene glycol reveal spatially invariant reorientation dynamics for all chromophores. Capping the silica support with Me2SiCl2 results in spatially invariant reorientation dynamics in the IL. We understand these data in the context of the IL exhibiting a spatially damped piezoelectric response mediated by IL fluidity and disorder.

Structural Determinants of Improved Fluorescence in a Family of Bacteriophytochrome-Based Infrared Fluorescent Proteins: Insights from Continuum Electrostatic Calculations and Molecular Dynamics Simulations.

Using X-ray crystallography, continuum electrostatic calculations, and molecular dynamics simulations, we have studied the structure, protonation behavior, and dynamics of the biliverdin chromophore and its molecular environment in a series of genetically engineered infrared fluorescent proteins (IFPs) based on the chromophore-binding domain of the Deinococcus radiodurans bacteriophytochrome. Our study suggests that the experimentally observed enhancement of fluorescent properties results from the improved rigidity and planarity of the biliverdin chromophore, in particular of the first two pyrrole rings neighboring the covalent linkage to the protein. We propose that the increases in the levels of both motion and bending of the chromophore out of planarity favor the decrease in fluorescence. The chromophore-binding pocket in some of the studied proteins, in particular the weakly fluorescent parent protein, is shown to be readily accessible to water molecules from the solvent. These waters entering the chromophore region form hydrogen bond networks that affect the otherwise planar conformation of the first three rings of the chromophore. On the basis of our simulations, the enhancement of fluorescence in IFPs can be achieved either by reducing the mobility of water molecules in the vicinity of the chromophore or by limiting the interactions of the nearby protein residues with the chromophore. Finally, simulations performed at both low and neutral pH values highlight differences in the dynamics of the chromophore and shed light on the mechanism of fluorescence loss at low pH.

Ultrafast Structural Evolution and Chromophore Inhomogeneity inside a Green-Fluorescent-Protein-Based Ca2+ Biosensor

Understanding excited-state structural dynamics of fluorescent-protein-based biosensors for Ca(2+) imaging is crucial for developing new in vivo Ca(2+) indicators and advancing bioimaging. We implemented wavelength-tunable femtosecond stimulated Raman spectroscopy (FSRS) with a 530 nm Raman pump to uncover the working mechanism of an intensiometric fluorescent-protein biosensor, G-GECO1.1, highlighting the deprotonation process of its embedded chromophore. Besides confirming the dynamic difference of excited-state proton transfer (ESPT) in the Ca(2+)-free/bound protein, we revealed a chromophore two-ring twisting process with time constants of 36/60 ps that competes with ESPT. In contrast with FSRS data collected using the 800 nm Raman pump, the bluer Raman pump enables us to access a subset of reactant population with partially deprotonated character that exhibits an additional ESPT component on the ∼5 ps time scale. These findings provide deep mechanistic insights into the inhomogeneity and subpopulation-specific conformational dynamics of biosensor chromophores, which will guide the rational design of improved biosensors for metal ion imaging.

Synthesis, structure, ultrafast kinetics, and light-induced dynamics of CuHETPHEN chromophores.

Five heteroleptic Cu(i)bis(phenanthroline) chromophores with distinct variation in the steric bulk at the 2,9-phenanthroline position were synthesized using the HETPHEN method, and their ground and excited state properties are described. Analysis of the crystal structures reveals a significant distortion from tetrahedral geometry around the Cu(i) centre which is attributed to favourable aromatic interactions between the two phenanthroline ligands. Ultrafast and nanosecond transient optical spectroscopies reveal that the excited state lifetime can be tuned across two orders of magnitude up to 74 nanoseconds in acetonitrile by changing the 2,9-substituent from hydrogen to sec-butyl. X-ray transient absorption spectroscopy at the Cu K-edge confirmed Cu(i) oxidation to Cu(ii) and revealed a decrease of the Cu-N bond lengths in the excited state. The ground and excited state characterization presented here will guide the integration of CuHETPHEN chromophores into complex electron donor-acceptor architectures.

Reorientation Dynamics of Chromophores in Photosensitive Polymers by Means of Coarse-Grained Modeling.

We study the photoisomerization of azobenzene chromophores embedded into a polymer matrix by using coarse-grained simulations. Two types of beads are considered: t- and c-beads, which are rich in trans and cis isomers, respectively. Simulations combine deterministic (molecular dynamics) and stochastic (random-type switching) parts. The ratio between the characteristic times for photoinduced reorientation and for orientation relaxation is tuned to be of the order found in experiments. The essential features of the phenomenon: 1) the existence of a stationary state, and 2) anisotropic distribution of the orientations of t-beads (orientation hole-burning effect), are reproduced. We study population dynamics of c-beads and the strength of the orientation hole burning, depending on the illumination wavelength and its intensity. The form of the reorientation potential of the mean force acting on the t-beads is analyzed and its use is validated.

Mimic of the green fluorescent protein β-barrel: photophysics and dynamics of confined chromophores defined by a rigid porous scaffold.

Chromophores with a benzylidene imidazolidinone core define the emission profile of commonly used biomarkers such as the green fluorescent protein (GFP) and its analogues. In this communication, artificially engineered porous scaffolds have been shown to mimic the protein β-barrel structure, maintaining green fluorescence response and conformational rigidity of GFP-like chromophores. In particular, we demonstrated that the emission maximum in our artificial scaffolds is similar to those observed in the spectra of the natural GFP-based systems. To correlate the fluorescence response with a structure and perform a comprehensive analysis of the prepared photoluminescent scaffolds, (13)C cross-polarization magic angle spinning solid-state (CP-MAS) NMR spectroscopy, powder and single-crystal X-ray diffraction, and time-resolved fluorescence spectroscopy were employed. Quadrupolar spin-echo solid-state (2)H NMR spectroscopy, in combination with theoretical calculations, was implemented to probe low-frequency vibrational dynamics of the confined chromophores, demonstrating conformational restrictions imposed on the coordinatively trapped chromophores. Because of possible tunability of the introduced scaffolds, these studies could foreshadow utilization of the presented approach toward directing a fluorescence response in artificial GFP mimics, modulating a protein microenvironment, and controlling nonradiative pathways through chromophore dynamics.

Electron Transfer in One- and Zero-Dimensional Nanooptofluidic Devices

Working in the same hallway as Prof. Wieckowski and his students for 22 years taught us to appreciate the beauty of heterogeneous electron transfer. We are now pursuing that appreciation through coupled electron transfer and spectroscopic probing of processes in zero- and one-dimensional nanostructures. One-dimensional architectures are explored in two formats: (1) a horizontal geometry in which a small number of nanochannels are arrayed at the top surface of a fluidic device so that optical spectroscopy can be employed to augment studies of electrochemistry at embedded planar electrodes; and (2) vertically-oriented nanopores supporting embedded annular nanoband electrodes (EANEs) in massively parallel high-density arrays. Because transport and electron transfer are intimately coupled, high efficiency (unit efficiency in many cases) electrochemical conversions can be achieved in many structures, and the horizontal geometry allows detailed measurements of the spatiotemporal distributions of electrochemical products for comparison with finite-element modeling.Zero-dimensional architectures are also being studied in two formats: (1) arrays of nanoconfined recessed ring-disk electrodes (RRDEs), in which redox cycling can be carried out at very high efficiency; and (2) electrochemically-active zero-mode waveguides (ZMWs), in which strongly confined optical fields can be coupled to single molecule electron transfer events in order to study the dynamics of single enzyme molecules and single redox-active organic chromophores. Nanoscale separation in RRDE arrays allows ultra-efficient coupling of counterpoised electron transfer processes at the bottom disk and upper ring electrodes in an attoliter-volume nanopore, processes that can be exploited for improving both sensitivity and selectivity in electroanalysis. In the other geometry, the Au optical cladding layer of a ZMW is used as the working electrode in order to couple the local potential to the fluorescence dynamics of molecules exhibiting large changes in emission quantum efficiency with redox state. These experiments allow the distributions of single molecule E eq values and other details of electron transfer reactions to be measured on a single molecule basis.

Chromophore Dynamics in the PYP Photocycle from Femtosecond Stimulated Raman Spectroscopy

Femtosecond stimulated Raman spectroscopy (FSRS) is used to examine the structural dynamics of the para-hydroxycinnamic acid (HCA) chromophore during the first 300 ps of the photoactive yellow protein (PYP) photocycle, as the system transitions from its vertically excited state to the early ground state cis intermediate, I0. A downshift in both the C7═C8 and C1═O stretches upon photoexcitation reveals that the chromophore has shifted to an increasingly quinonic form in the excited state, indicating a charge shift from the phenolate moiety toward the C9═O carbonyl, which continues to increase for 170 fs. In addition, there is a downshift in the C9═O carbonyl out-of-plane vibration on an 800 fs time scale as PYP transitions from its excited state to I0, indicating that weakening of the hydrogen bond with Cys69 and out-of-plane rotation of the C9═O carbonyl are key steps leading to photoproduct formation. HOOP intensity increases on a 3 ps time scale during the formation of I0, signifying distortion about the C7═C8 bond. Once on the I0 surface, the C7═C8 and C1═O stretches blue shift, indicating recovery of charge to the phenolate, while persistent intensity in the HOOP and carbonyl out-of-plane modes reveal HCA to be a cissoid structure with significant distortion about the C7═C8 bond and of C9═O out of the molecular plane.

Effects of intramolecular hydrogen bonding on the excited state dynamics of phenol chromophores

The theoretical prediction and experimental confirmation of the 1πσ* excited state of phenol which is repulsive along the O-H bond has a large impact on the interpretation of phenol and tyrosine photochemistry. In this work, we demonstrate that this excited state changes significantly if the OH functional group is involved in the formation of an intramolecular hydrogen bond in the ground state. We investigate the excited state dynamics of 2-, 3-, and 4-hydroxyacetophenone (HAP) separately in a molecular beam at 193 nm using multimass ion imaging techniques. H atom elimination from the repulsive excited state and Norrish type I reactions are the major dissociation channels of 3-HAP and 4-HAP which do not have intramolecular hydrogen bonding. However, the H atom elimination channel is completely quenched for 2-HAP which shows intramolecular hydrogen bonding. In addition, the ground state and the excited state potential energy surfaces (PESs) of HAP, 2-hydroxybenzoyl fluoride, 2-hydroxybenzoyl chloride, and 2-hydroxybenzamide are investigated using ab initio calculations. The results also show that the excited state potential along the O-H bond distance of the hydroxyl group changes significantly for molecules with intramolecular hydrogen bonding. The changes include: (a) the repulsive potential energy surface becomes an attractive potential near the ground state equilibrium geometry, (b) the conical intersection between the first and the second excited states along the O-H bond moves to a much higher energy level, and (c) the conical intersection between the repulsive excited state and the ground state along the O-H bond distance disappears. The results suggest that the interpretation of the photochemistry for molecules with a phenol chromophore must take these effects into consideration.

Photodissociation dynamics of methoxybenzoic acid at 193 nm

The theoretical prediction and experimental confirmation of the 1πσ* repulsive excited state along O-H bond of phenol have large impact on the interpretation of phenol and tyrosine photochemistry. In this work, we investigated the photodissociation dynamics of 2-, 3-, and 4-methoxybenzoic acid (MOBA) in a molecular beam at 193 nm using multimass ion imaging techniques. In addition, the ground state and the excited state potential energy surfaces of MOBA were investigated using ab initio calculations, and branching ratios were predicted by Rice-Ramsperger-Kassel-Marcus theory. The results show that (1) the excited state potential of 1πσ* along O-CH(3) bond remains similar to that of phenol and anisole, (2) CH(3) elimination is the major channel for three MOBA isomers, and (3) photofragment translational energy distributions show bimodal distributions, representing the dissociation on the ground state and repulsive excited state, respectively. Comparison to the study of hydroxbenzoic acid [Y. L. Yang, Y. A. Dyakov, Y. T. Lee, C. K. Ni, Y. L. Sun, and W. P. Hu, J. Chem. Phys. 134, 034314 (2011)] shows that only the intramolecular hydrogen bonding has significant effects on the excited state dynamics of phenol chromophores.

Exploring Ultrafast H-Atom Elimination versus Photofragmentation Pathways in Pyrazole Following 200 nm Excitation

The role of ultraviolet photoresistance in many biomolecules (e.g., DNA bases and amino acids) has been extensively researched in recent years. This behavior has largely been attributed to the participation of dissociative (1)πσ* states localized along X-H (X ═ N, O) bonds, which facilitate an efficient means for rapid nonradiative relaxation back to the electronic ground state via conical intersections or ultrafast H-atom elimination. One such species known to exhibit this characteristic photochemistry is the UV chromophore imidazole, a subunit in the biomolecules adenine and histidine. However, the (1)πσ* driven photochemistry of its structural isomer pyrazole has received much less attention, both experimentally and theoretically. Here, we probe the ultrafast excited state dynamics occurring in pyrazole following photoexcitation at 200 nm (6.2 eV) using two experimental methodologies. The first uses time-resolved velocity map ion imaging to investigate the ultrafast H-atom elimination dynamics following direct excitation to the lowest energy (1)πσ* state (1(1)A" ← X(1)A'). These results yield a bimodal distribution of eliminated H-atoms, situated at low and high kinetic energies, the latter of which we attribute to (1)πσ* mediated N-H fission. The time constants extracted for the low and high energy features are ~120 and <50 fs, respectively. We also investigate the role of ring deformation relaxation pathways from the first optically bright (1)ππ* state (2(1)A' ← X(1)A'), by performing time-resolved ion yield measurements. These results are modeled using a (1)ππ* → ring deformation → photofragmentation mechanism (a model based on comparison with theoretical calculations on the structural isomer imidazole) and all photofragments possess appearance time constants of <160 fs. A comparison between time-resolved velocity map ion imaging and time-resolved ion yield measurements suggest that (1)πσ* driven N-H fission gives rise to the dominant kinetic photoproducts, re-enforcing the important role (1)πσ* states have in the excited state dynamics of biological chromophores and related aromatic heterocycles.

Extracting Spectral Dynamics from Single Chromophores in Solution

Fluorescence spectroscopy of single chromophores immobilized on a substrate has provided much fundamental insight, yet the spectral line shapes and dynamics of single chromophores freely diffusing in solution have remained difficult or impossible to measure with conventional linear spectroscopies. Here, we demonstrate an interferometric technique for extracting time dependent single chromophore spectral correlations from intensity correlations in the interference pattern of an ensemble fluorescence spectrum. We apply our technique to solutions of colloidal quantum dots and explore the spectrum of single particles on short time scales not feasible with conventional fluorescence measurements.

Effects of Ethanol on the Organization of Phosphocholine Lipid Bilayers

We have investigated the consequences of the addition of ethanol to aqueous solutions containing 100 nm diameter phosphocholine unilamellar vesicles. We have studied the effect of ethanol addition on both gel phase and fluid phase phospholipid bilayers of 1,2-dimyristoyl-sn-phosphatidylcholine (DMPC), using time-resolved fluorescence measurements of perylene incorporated into the vesicles. We observe an increase in the perylene rotational diffusion time constants for ethanol concentrations of ca. 0.6 M in both the gel phase (289 K) and the fluid phase (303 K), indicating a change in the bilayer interacyl chain spacing and/or organization. While the change in rotational diffusion behavior of perylene is seen for both phospholipid phases, the details of the change in chromophore dynamics are not the same for the two phases, likely due to the differing extents of disorder in the phospholipid acyl chain region at the two temperatures. These data provide insight into the effects of ethanol on the local environment of the probe in both gel phase and fluid phase lipid bilayers.

Photostability of amino acids: photodissociation dynamics of phenylalanine chromophores

The theoretical prediction of H atom elimination on the excited state of phenol, imidazole and indole, the respective chromophores for the amino acids tyrosine, histidine and tryptophan, and the confirmation of theoretical prediction by experimental observations have a great impact on the explanation of photostability of amino acids upon irradiation with UV photons. On the other hand, no theoretical prediction of the excited state photodissociation dynamics has been made on the other aromatic amino acid, phenylalanine. In this work, photodissociation dynamics for various phenylalanine chromophores, including, phenylethylamine, N-methyl-phenylethylamine, and N-acetyl phenylalanine methyl ester was investigated in a molecular beam at 248 and 193 nm using multimass ion imaging techniques. The major dissociation channel for these compounds is the C-C bond cleavage. However, the photofragment translational energy distribution of phenylethylamine contains two components. The slow component corresponds to the dissociation on the ground state surface after internal conversion, and the fast component represents the dissociation from an excited state with a large exit barrier. The competition between the dissociation on the ground state and on the excited state changes as the size of chromophores increases. Internal conversion to the ground state prior to dissociation becomes the major nonradiative process for large chromophores. This study reveals the size-dependent photostability for these amino acid chromophores.

Effect of Hydrogen Bonding on the Rotational and Translational Dynamics of a Headgroup-Bound Chromophore in Bilayer Lipid Membranes

We have studied the interactions of the chromophore 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-7-nitro-2-1,3-benzoxadiazol-4-yl (18:1 NBD-PE) imbedded in the headgroup region of bilayer lipid membranes consisting of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DOPG). We have examined the molecular and mesoscale dynamics of the chromophore using time-correlated single photon counting (TCSPC) to measure rotational diffusion dynamics in lipid vesicles and fluorescence recovery after pattern photobleaching (FRAPP) to determine translational diffusion coefficients and mobile fractions in supported lipid bilayers. TCSPC data reveal that chromophore rotational diffusion rates in DOPG vesicles are statistically the same as in DOPC and mixed DOPC/DOPG vesicles, suggesting that the NBD-PE chromophore does not interact strongly with the headgroup region of these bilayers; however, FRAPP experiments show that lateral diffusion is statistically lower in mixed DOPC/DOPG-supported bilayers than in DOPC-supported bilayers. These results suggest that bilayers containing DOPG likely undergo interlipid headgroup hydrogen bonding interactions that suppress translational diffusion.

Constituent-Dependent Liposome Structure and Organization

We have used steady state and time-resolved fluorescence spectroscopy in concert with TEM to study organization and dynamics of molecules comprising liposomes, discoidal micelles, and spherical micelles. The lipid aggregates contained controlled amounts of lipids with headgroups modified with a thiol-terminated polyethylene glycol (thio-PEG lipids) and a small amount of 1-palmitoyl-2-(pyrene-1-yl)decanoyl-sn-glycero-3-phosphocholine (pyrene tethered DPPC), pyrene, or perylene as spectroscopic probes. The maximum diameter of the lipid aggregates was controlled by the polycarbonate filter pore size used in the extrusion process. The concentration of thio-PEG lipid in the aggregates determines not only the shape of the lipid assemblies but also the organization of the molecules within the assembly. Fluorescence lifetime and anisotropy decay data show that the immediate environment of pyrene tethered DPPC changes with the addition of thio-PEG lipid. In contrast, the dynamics of free chromophore (perylene) are insensitive to the addition of thio-PEG lipid. The addition of thio-PEG lipid to the lipid assembly produces changes in organization that are most pronounced in the lipid headgroup region. Reorientation dynamics of perylene show that the organization of the lipid bilayer acyl chain region is affected little by the addition of thio-PEG lipid and consequent macroscopic changes in the morphology of the lipid assemblies.

Efficient Calculation of Time- and Frequency-Resolved Four-Wave-Mixing Signals

"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.