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July 30, 1997 10:42 Annual Reviews AR040-10

Annu. Rev. Phys. Chem. 1997. 48:271–97Copyright c© 1997 by Annual Reviews Inc. All rights reserved

TWO-PHOTON–INDUCEDFLUORESCENCE

Patrik R. CallisDepartment of Chemistry and Biochemistry, Montana State University, Bozeman,Montana 59717; e-mail: [email protected]

KEY WORDS: lasers, three-photon, molecular electronic spectroscopy, alternant hydrocarbons,multiphoton ionization

ABSTRACT

Nonresonant two-photon electronic spectroscopy of polyatomic molecules is re-viewed for the period since 1979. Emphasis is placed on studies that exposepatterns in the two-photon fluorescence (also ionization, optoacoustic) excitationspectra of aromatic hydrocarbons and the effect of vibrations and substitution,particularly within the framework of pseudoparity rules. A section is devoted tobiological molecules and the emerging use of two-photon–induced fluorescenceanisotropy. Relevant theoretical results are discussed, with emphasis on quantumchemical predictions of vibronic coupling and substituent effects on two-photonabsorptivity and tensor properties of individual molecules. This chapter includeshigher-order spectroscopy, and a limited number of three- and four-photon studiesare discussed.

INTRODUCTION AND SCOPE

Nonresonant two-photon electronic state spectroscopy has provided a rich com-plement of electronic structure information, comparing to ordinary one-photonspectroscopy as Raman scattering does to IR absorption. The increased avail-ability of powerful picosecond and femtosecond pulsed, tunable laser systemsduring the last decade has transformed two-photon spectroscopy from a rela-tively exotic arena to one that is routine. Indeed, since the late 1970s, the systemsthat could be studied by two-photon spectroscopy have evolved from crystals orconcentrated solutions and gases to molecular beams, rare-gas matrices, and ul-tra dilute solutions—even at the single-molecule limit. Two-photon excitation

2710066-426X/97/1001-0271$08.00



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(TPE) is now used in a wide variety of studies, including rotationally resolvedspectra, time-resolved anisotropy, fluorescence microscopy, photochemistry,chemical analysis, chromatographic detection, and in vivo sampling, to name afew. Friedrich (1) and Birge (2, 3) have published introductory expositions ofTPE, and Lin et al (4) have completed a comprehensive treatment of its theoryand techniques.

This review is concerned with two-photon (and some three- and four-photon)electronic state spectroscopies, wherein neither of the photons alone is resonantwith an energy eigenstate of the molecule. Its primary focus is experimental flu-orescence excitation spectra, but it also includes discussion of important studiesthat employ ionization, acoustic, thermal lensing, and photochemical detection.While some effort is made to recognize useful developments in experimental andtheoretical techniques, emphasis is on innovations and insightful applications tothe understanding of larger molecules, including those encountered in biophysi-cal studies, occurring since the review by Friedrich & McClain (5) in 1980. Thisof course excludes a massive amount of work in the area of diatomic moleculesas well as atomic and solid state physics, and the usual apology is extended forother omissions, whether due to painful choice or to an imperfect search.

Regardless of the type of molecule and means of detection, one of the mostuseful tools associated with multiphoton excitation has continued to be a typeof polarization ratio,�, defined as the ratio of absorptivities using circularlyand linearly polarized excitation light (6):

�(n) = δcir/δlin .

� is directly related to the trace squared of the two-photon tensor relative tothe sum of squares of all the elements of the tensor, andn is the number ofphotons absorbed simultaneously. For two photons when the detected sig-nal is integrated to remove any anisotropies, the limits of� are from zero(when the tensor is proportional to the identity matrix) to 3/2 (trace is zero) (6).Two-photon transitions from a totally symmetric ground state to a nontotallysymmetric state are required to have� = 3/2, while for those to a totallysymmetric state may have any value in the range 0 to 3/2 (6).

TPE spectroscopy has played an important pedagogical role, being the firstof the multiphoton excitation spectroscopies. The seminal work of McClain (7)has spawned extensions to useful three- and four-photon experiments. Dye lasertechniques were developed for producing accurate excitation spectra over theentire visible range and beyond, along with simultaneous measurement of�,thereby allowing several electronic states to be probed for any given molecule.Systematic studies exposed unexpected patterns, which stimulated theoreticalactivity. This has been particularly true for aromatic hydrocarbons and their



TWO-PHOTON FLUORESCENCE 273

derivatives, where a universal understanding of the effect of substitution andvibronic coupling based on pseudoparity-dictated transition density patternswas established for excitations by any number of photons.

Basic Symmetry ConsiderationsThe operator responsible for ann-photon transition is proportional toxi y j zk,wherex, y, andz are the electron Cartesian positions and the integersi, j, andk must sum ton, the order of the multiphoton process. It is always true thatthe direct product symmetry must contain the irreducible representation of thetransition operator. For centrosymmetric systems, the inversion symmetry ofthe Cartesian coordinates leads to the familiar parity selection rules: u↔ gfor odd n and g↔ g or u↔ u for evenn. This review, however, is equallyconcerned with the larger class of molecules withC2v or lower symmetry, forwhich all two-photon transitions are allowed, and addresses patterns of strongand weak two-photon intensities for these allowed transitions. For this reason,the pseudoparity rules (+ ↔ − for oddnand+↔ +,− ↔ − for evenn) havetaken a spotlight in multiphoton studies of most conjugated hydrocarbons, andare discussed next.

NEUTRAL ALTERNANT HYDROCARBONS

Pseudoparity and Transition Density PatternsAlternant hydrocarbons are characterized by conjugatedπ systems with noodd-numbered rings. Model Hamiltonians such as H¨uckel and Pariser-Parr-Pople (PPP) that assign theπ atomic orbitals (AOs) a constant diagonal energyand recognize interactions between bonded AOs only, give rise to a pairing ofoccupied and unoccupied molecular orbitals (MOs) and their energies, whichin turn leads to two noninteracting classes of states. These were designated+and− by Pariser (8), with the ground state and covalent excited states turningout to be “−,” while ionic states were “+”. These designations are commonlycalled pseudoparity (9, 10) but have been discussed as part of a general alternantsymmetry (11). Note that the signs are reversed in some uses (for example see12). They have proven particularly useful because they carry implicationsregarding the strength of generic perturbations, e.g. inductive substitutions,cross-linking, and vibrational distortions (9).

Two-photon spectroscopy has removed an experimental bias in the under-standing of aromatic hydrocarbon spectra, a bias due to the nature of the easilystudied1L−b (B−2u) state of substituted benzenes. We are accustomed to thinkingof vibronic coupling as a weak effect that never involves the ground state, and toseeing inductive effects cause large perturbations to the spectrum. That the re-verse of this behavior was true in the early TPE spectra of the1L−b –S0 transition



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for every molecule studied motivated the rediscovery and generalization (9, 13)of underlying principles summarized in the papers by Moffitt (14) and Doneth(15) for one-photon absorption (OPA). Briefly, the key theorem (15) is that first-order transition density matrices (in theπ AO basis) representing the productof two states with the same pseudoparity will have no diagonal elements butcan have off-diagonal elements between bonded AOs, whereas the reverse istrue when the two states have opposite pseudoparity. The coupling betweentwo states by one-electron operators can be expressed as a simple projectionof the transition density matrix and the perturbation matrix, i.e. their overlap(9, 16). This means that inductive perturbations and transition dipoles (whichhave diagonal matrices) will be effective at coupling only states of oppositepseudoparity, while the reverse is true for bond-stretching distortions. In thefollowing discussions, a constant theme is strong two-photon enhancement ofthe1L−b –S0 transitions by vibronic coupling with the ground state and the lackthereof for1L+a ; the reverse is true for inductive perturbations (9). Note that inthe Platt classification, the1L−b –S0 transition density is in the bonds while thatfor 1L+a –S0 is in the atoms—independent of group theory labels and axis choice.

BenzeneBenzene received much attention from two-photon spectroscopists during the1980s. The spectacular difference between the OPA and TPE spectra of theS1system (1B−2u or 1L−b ) caused by the unexpected strong Herzberg-Teller (HT)false origin built on the b2umodeν14(17–19) became a paradigm in itself for theTPE of the1L−b –S0 transition of all neutral alternant hydrocarbons, includingthose with substitution. Extensive experimental TPE and theoretical evidencenow exists to show that this mode, called the Kekule mode because it alternatelycompresses and stretches the C-C bonds, strongly couples the ground and1L−bstates. As a consequence, its frequency is higher in the excited state than in theground state, typical of a pseudo Jahn-Teller effect. Indeed, from a valence bondview, this mode is the coordinate of an avoided crossing of the two Kekule energysurfaces (20, 21). One of the characteristics of theν14 false origin is its low�(only 0.05 in vapor and≈0.25 in liquid). I further discuss this mode below.

Murakami et al (22) and Aron et al (23) performed the first TPE of the1L−b –S0 transition of benzene under supersonic jet–cooled conditions usingtwo-photon resonant multiphoton ionization, [(2+ 2) MPI]. Six members oftheν14-based progression were observed, i.e. up to 141

0150, 6165 cm−1 above the

origin, which was considerably higher than could be seen using fluorescencedetection. The rotational temperature in the study by Aron et al (23) was about1 K. The vibronic lines appeared to broaden to 100 GHz (3.3 cm−1) for thosein the “channel three” region with excess energy above 3100 cm−1, where thefluorescence quantum yield drops precipitously.




Riedle, Neusser, and coworkers (24–33), in a brilliant decade-long study ofthe channel three phenomenon, measured the first Doppler-free two-photonfluorescence excitation of a polyatomic molecule, observing homogeneouslinewidths at a resolution of 5 MHz with CW excitation and at a resolutionof 70 MHz with pulsed excitation, the latter yielding lifetime measurements(see 33 for an overview). At low excess energy, the rotational structure is com-plete, with a few extra lines broadened and split by resonances with dark states.The experimental finding for 141

0120 (3412 cm−1 excess energy), however, shows

a drastically reduced number of lines, with onlyK = 0 lines appearing for lowJ, and onlyK = J lines appearing for highJ. This remarkable result led Helman& Marcus (34) to a unified model involving anharmonic Coriolis coupling inS1plus internal conversion toS0, with S1 not in the statistical limit. At lowJ, thepathway is parallel Coriolis coupling (small forK = 0) of the initially excitedin-plane modes to those in-plane modes that have cubic anharmonic couplingto the out-of-plane modes with large Franck-Condon (FC) factors to the highvibrational levels ofS0. The highJ limit is dominated by double perpendicularCoriolis couplings (small forK = J) directly to the out-of-plane modes.

Faidas & Siomos (35) conducted an excellent two-photon fluorescence exci-tation study of dilute solutions of benzene and toluene in a variety of solventsover the two-photon energy range 35,700 to 55,500 cm−1. In perfluorohexanethe spectra are nearly as sharp as in vapor, with the added advantage of fairly con-stant quantum yields throughout, in contrast to vapor where almost no fluores-cence is seen for excitation energies>3100 cm−1 above the origin. This studyfilled a large assignment gap for the1L−b state, and captured interesting featuresconcerning the higher electronic states and the solvent-induced origin, whichare discussed below. Their study confirmed earlier TPE spectra of neat benzeneand toluene using fluorescence (10, 36) and optoacoustic detection (37).

In stark contrast to OPA, the TPE of the1L+a (1B1u)–S0 transition, beginningnear 46,500 cm−1, was found to be several times weaker than the1L−b bandin several investigations (10, 35, 36, 38). Bree et al (39) measured the TPEspectrum of benzene single crystals at 4.2 K, finding broad vibronic structuredistinct from that in the corresponding one-photon spectrum. At least threeother studies spanned theS2 region and higher energies to about 55,000 cm−1.Those in neat benzene and in hydrocarbon or tetramethylsilane solvent showedstrong TPE in the 380-nm region about 100 times that in the 410-nm region.Ziegler & Hudson (40) assigned this intensity to vibrationally induced transi-tions of the two-photon forbidden1E1u state on the basis of� values and thesimilarity to the one-photon spectrum. Scott & Albrecht (41), however, pre-sented convincing evidence through solvent and temperature dependence thatthis is the 3s← e1gRydberg transition, which is so evident in the vapor, still be-ing expressed in condensed phase. Here again two-photon spectroscopy offers



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a view that is obscured in the UV spectrum. The Faidas-Siomos’ spectra (35)are in good agreement, provided quantum yield variations are considered. Scottet al (42) studied the three-photon ionization spectrum of liquid benzene andquantitatively determined the ratio of the TPE spectra for fluorescence versusionization spectrum. The authors concluded from temperature and electric fieldstudies that the highly excited states reached after absorption of the third photonby the benzene excimer collapse into geminate charge pairs, which thermallydissociate to free charge carriers.

At even higher energies, hard evidence for the long-sought1E2g (ππ∗) stateof benzene was found in the (2+ 1) MPI spectrum by Whetten et al (43), withthe origin at 60,800 cm−1. This state appears to be highly mixed with Rydbergs.Other Rydberg series were uncovered (44).

Goodman and coworkers (45–51) took advantage of the considerable hydro-gen motion in the modes that induce the TPE of benzene to extend knowledgeof ground and1Lb vibrations by deuterium substitution. Mode scrambling andDuschinsky effects were observed for the pairsν14,ν3 andν18,ν9. Examinationof the 14101n

0 progression for benzene-h6 and benzene-d6 revealed thatν1 wasmore anharmonic in the deuterated molecule. This was explained on the basis ofa larger proportion of C-D stretching in the deuterated molecule. Measurementof the ratio of the 1510/141

0 vibronic two-photon cross sections for a series ofisotopically labeled benzenes proved to be in good agreement with predictionsfrom theB2u force field and led to a harmonic sum rule for the TPE intensities(49). However, the main goal of their study, to determine experimentally therelative phase of the hydrogen motions in the two modes, eluded them becauseit was masked by theν14-ν15 anharmonicity.

Catacondensed AromaticsIn the early 1980s, Hohneicher & Dick (52–55) and, independently, Razumova& Starobogatov (56, 57) led the way in an impressive experimental surveyof the two-photon fluorescence excitation spectra of the family of polycyclicaromatic hydrocarbons in dilute solution, including naphthalene (52, 53, 56),anthracene (52, 54, 56), tetracene (57), phenanthrene (52, 55, 56), and relatedsystems, toluene (36, 52), acenaphthene (53), biphenyl (52). Their studies wereoften exemplified by wavelength ranges of unprecedented size (400–685 nm)and always accompanied by measurement of�. Salvi and coworkers addedsimilar investigations of pyrene (58), anthracene (59), and chrysene (60). Onepervading observation in almost every study was the observation of a strongfalse origin in the1L−b band with low� and with frequency≈1500 cm−1.Another pattern was that the1L−b band was always more prominent than the1L+a , a large difference from the one-photon spectra. For anthracene, Razumova& Starobogatov (56) were the first to observe the spectacular near absence of




the1L+a origin at 26,700 cm−1 and to surmise correctly that the strong peak at29,100 cm−1 was a false origin of the1L−b band induced by the correspondingKekule vibration. Their assignment was reinforced by experiments and analysisby Salvi & Marconi (59, 61, 62). An exception to the pattern seems to have beenfound by Yu et al (63), whose TPE and� spectrum for perylene, correspondingto UV wavelengths 425 to 265 nm, shows the lowest energy peak to have a high� (� = 1.4). This peak is∼3500 cm−1 above theS1(L

+a ) origin.

Much stronger bands at shorter wavelengths not coinciding with the strongUV bands were assigned to TPE-allowed gerade states using� values as aguide for symmetry, usually with the aid of semiempirical electronic struc-ture calculations. Such symmetry assignments are compromised, however,by overlapping bands, possible vibronic coupling, and the inability of� todistinguish absolutely between total and nontotal symmetry when� ∼ 3/2.Two extreme examples of interpretation can be noted. Liem et al (60, 64)assigned the strong peak at 301 nm with� = 1.4 (� = 1.23 according to Ref-erence 65) in the TPE of chrysene as vibrationally induced 2A−g × ag, with the2A−g origin approximately sixfold weaker at 315 nm and� = 0.9, presumablybecause their CNDO/S-CI calculations found too fewA−g states and indicatedlarge zero trace vibronic intensity for 2A−g . If true, this assignment marks anew paradigm wherein a nominally allowed transition has HT coupled intensityby an ag mode that is an order of magnitude stronger than the Kekule modecoupling of1Lb–S0, and provides a large zero-trace component to the tensor. Atthe other extreme, Ramasesha et al (12) have reassigned the peak in anthraceneat 30,800 cm−1 as 2A−g (instead of1Lb× b2u) because it has low� and becausetheir complete-CI PPP calculations place 2A−g at 31,260 cm−1, disregarding thepossibility of significant vibrationally induced bands.

A second wave of progress was marked by the study of many of thesemolecules as dilute guests in single crystal environments or Shpol’skii matrices(64, 66–72), in some cases yielding resolutions to 4 cm−1 with site-selectivetechniques (for example, see 68). These studies have contributed greatly to theunderstanding of the vibrational modes of the lower excited states. Bree et al(67) used information on ag modes from the TPE of pyrene to clarify issuesraised in one-photon spectra where these modes are both FC and HT active.The most elegant study to date is that of Wolf & Hohlneicher (69), who appliedtheir powerful site selection technique to anthracene in Ar at 12 K. With one-photon excitation (OPE), the1L+a (B

+1u) origin location varied over a range of

225 cm−1 for different sites. They found the1L−b origin to be completely miss-ing in the TPE for two of the three sites studied. The strong lines correspondingto the Kekule false origin were found to be at least 10 times less sensitive toenvironment, thereby providing a convincing, independent piece of evidencethat these lines do not belong to the1L−b system. Using the relative solvent



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shift information, they extrapolated the location of the1L−b origin location tobe only 350± 50 cm−1 above that of1L+a in vacuum. No evidence for thesymmetry-allowed1L−b origin could be found in their OPE spectrum, in spiteof the unprecedented sensitivity and resolution commanded in this experiment.This is an example of extreme adherence to the pseudoparity rule.

Related alternant hydrocarbons studied by TPE include stilbene (73), biphe-nylene (74), and tolan (75).

PolyenesTwo-photon spectroscopy continues to play an important role in developingknowledge of low-lying electronic structure of linear polyenes. By the early1980s, two-photon spectroscopy had played a crucial role in elucidating thenature of the close-lyingS1(A−g ) and S2(B+u ) states. Kohler and coworkers(76–85) have continued to exploit the centrosymmetric sites of solidn-octaneandn-hexane hosts, for which a rigorous division into ungerade and gerade finalstates holds for OPE and TPE, respectively. As with earlier work on all-transoctatetraene, it is found thatcis-cisoctatetraene also maintains strict centrosym-metry in these hosts and exhibits only 11B+u or 21A−g origins for OPE and TPE,respectively, which are similar in energy to those of the all-transform (78).

Beautiful jet-cooled OPE and TPE of the all-transisomers of 1,3,5,7-octate-traene, 1,3,5,7-nonatetraene, and 2,4,6,8-decatetraene have been obtained re-cently by Petek et al (86, 87). This study provides examination of the 2A−g stateof these molecules at an unprecedented level of detail and strongly reinforcesand complements the extensive condensed phase work.

The TPE spectrum of all-transoctatetraene inn-octane andn-hexane has beenextended recently to 50,000 cm−1 (85). From 28,000 to 44,000 cm−1, all bandswere shown to be vibronic bands of the 21A−g –11A−g transition. At least two new0-0 transitions to higherm1A−g states were found (at 45,030 and 46,710 cm−1).

An intriguing parallel exists between the 2A−g state of linear polyenes and the1L−b state of perimeter aromatic hydrocarbons, which exhibit large transitiondensity elements between the atoms with alternating phase. In both classes,there is an alternating phase-stretching vibration that appears to couple theseexcited states with the ground state, as deduced by the large frequency increasein the mode upon excitation. Mixing with the ground state provides a potentsource of two-photon absorption (TPA) amplitude, and in the aromatic systems itoverpowers most substitutional perturbations that render the1L−b –S0 transitiontwo-photon allowed. An important difference in the polyene case is that thisinducing mode is totally symmetric, and there is experimental and theoreticalevidence that excitation to 2A−g causes a large geometry change along thismode, making it FC active as well as HT active. If the two sources of intensityare comparable, they will interfere, causing a non-Poissonian progression anda lack of mirror symmetry in the fluorescence (88).




TPE spectra of diphenylbutadiene have been obtained in ether:pentane:ethanol (EPA) glass (89) and in jet (80, 81, 90). In the glass, the 21A−g stateis only 130 cm−1 below the 11B+u state. In the jet (81), the TPE is much lesscomplicated than the OPE spectrum, having progressions only in displaced agvibrations. The TPE results were used to assign several additional bu funda-mentals. Detailed dynamics behavior (81, 90) and resonance-enhanced hyper-Raman scattering (80, 81) were also studied in the jet.

McDiarmid and coworkers have reported fruitful two-photon–based studiesof the 3s, 3p, 3d, and 4s Rydberg states of hexatriene (91, 92) and of the NV2 and3s Rydberg states of norbornadiene (93, 94). Associated vibrational structurewas also analyzed.

Perturbed Alternant Hydrocarbonsπ∗ →π TRANSITIONS The TPE of substituted benzenes has been effectively re-viewed by Goodman & Rava (13, 95–97), who carried out definitive systematicexperimental and theoretical studies on the1L−b state of benzene. They foundthat chlorine, bromine, and methyl groups were nearly 10 times as effectiveas fluorine at inducing allowed TPE intensity, although the 0-0 intensity wasstill less than that of the vibrationally induced 141

0 transition. They concludedthat OPE correlates primarily with the inductive effect (increasing from Br toF), while TPE correlates with the resonance interaction (increasing from F toBr) (96). The amino group, which has a much stronger resonance interaction,induces two-photon intensity nearly 10 times that of 141

0, while hydroxy is in-termediate (96). Similar experiments on phenylsilane (98) and benzotrifluoride(99) are in harmony with these results.

The pattern of constructive and destructive interference of interactions result-ing from multiple substitution is also complementary to that seen in OPE (95).Most striking is that 1,2,3-tri substitution makes1Lb–S0 symmetry allowed forboth TPE and OPE but is predicted and observed to be extremely weak in OPAand to be the strongest in TPE spectra.

Hollas et al (100, 101) reported more detailed TPE studies ofS1–S0 for ortho-andmeta-difluorobenzenes. As predicted (13, 95), they found that� = 3/2 forthe 0-0 transition of theorthocase—even though this is anA1← A1 transition.This represents another case wherein group theory allows� to be less than 3/2,but the specifics of the perturbation do not induce an isotropic (rank-0) compo-nent into the two-photon tensor. (See the discussion on phenanthrene, above.)

Stronger resonance perturbations of the benzene1L−b state in the form ofstyrene, phenyl acetylene, and benzonitrile fit the above pattern (13, 102, 103).Whereas styrene and phenyl acetylene have weak1L−b OPA, their TPA 0-0 inten-sities are comparable to that of 141

0. The inductive perturbation of transformingphenyl acetylene to benzonitrile increases the OPA by tenfold, while the TPAspectrum and intensity are virtually unchanged.



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Prompted by the pseudoparity prediction that the effects of vibrational andinductive effects would be reversed for the1L+a state, Scott et al (10) foundthat indeed the1L+a –S0 TPE band of benzene was greatly enhanced by fluorosubstitution. Rice & Anderson (38) conducted an important two-photon thermallensing study that spanned both the1L−b and1L+a regions for the series benzene,fluorobenzene, toluene, phenol, and aniline neat liquids. The results generallyagree with the earlier studies (10, 13) and uniquely show that hydroxy and aminoinduce five to ten times more TPA intensity into1L+a than into1L−b . Jones& Callis (104) further tested the pseudoparity rules by examining the TPE offluoro-, chloro-, and azanaphthalenes in solution, finding that the1L+a band wasstrongly enhanced in proportion to the inductive strength, while the1L−b bandwas virtually unchanged. Chlorine was found to have a moderate effect on bothtransitions, in accord with its having both inductive and resonance interactions.

SOLVENT EFFECTS The solvent-induced TPE intensity and� of forbiddentransitions offers the potential for improved microscopic understanding of sol-vation. Friedrich et al (105) noted that the1L−b origin in the TPE of benzene invarious solvents was quite conspicuous (about 50% the intensity of the most in-tense lines with circular polarization). In vapor, the origin is rigorously absent,as predicted fromD6hsymmetry. The�value for the solvent-induced origin wasfound to be 0.6–0.7 in a variety of solvents (35, 105), but this has not been ex-plained theoretically. Wirth and coworkers have studied the solvent dependenceof � for several larger hydrocarbons (65, 106). Bree and coworkers (71, 72)have studied the TPE of the1Lastate of anthracene induced by crystalline hosts.

π∗ → n TRANSITIONS The extensive review by Innes et al (107) includes evi-dence based on two-photon studies for several azabenzenes. Searching for theone-photon–forbidden, two-photon–allowed lowest1A2 (π∗ ← n) transition ofpyrimidine, Callis et al (108) found the strongest TPE band to peak at 42,500cm−1, 1500 cm−1 blue of the strong OPA1Lb–S0 transition, but with the samewidth as the OPA band. It was assigned as nearly pure b2 vibrationally inducedintensity, with the aza perturbation having little effect on the intensity relative tobenzene. The one- and two-photon versions of theS1 (1B1, π

∗ ← n) band werenearly identical and both about five times weaker than the corresponding1Lbintensity. The 11A2 (π∗ ← n) was assigned at 45,000 cm−1, on the high-energyshoulder of the1Lb band, visible only by increased�. The relative intensitiesrequired for these assignments are in accord with semiempirical (108) and abinitio (109) predictions. A careful gas-phase TPE polarization study by Knothet al (110) of theS1–S0 transition of pyrimidine revealed the vibrationally in-duced 1610 b1 line not seen in OPA. The same authors studied the two-photon–forbiddenS1 (π∗ ← n) band of pyrazine, observing vibronically active b3u and




b1u modes. The TPE ofS1 (π∗ ← n)–S0 transition ofsym-triazine was ob-tained using photoacoustic (111, 112) and MPI (113) detection. These studiesconfirmed the1E′′ (two-photon allowed) assignment for this state and offeredcontrasting interpretations of the complicatedν6 progression.

INDOLES

Because of its five-membered ring, indole is not formally a perturbed alternanthydrocarbon, and accordingly, pseudoparity rules are not found to be useful.The first TPE spectrum of indole (114), the chromophore of the amino acidtryptophan, demonstrated that�was different for the1Laand1Lb states, therebyproviding an excellent tool for studying the behavior of the two overlappingstates in fluid solution. It was also shown that the two-photon absorptivity forboth states was several times that for benzene. Rehms & Callis (115) measuredthe polarized TPE spectra of 5-methylindole, indole, 3-methylindole (3MI), and2,3-dimethylindole in cyclohexane and in butanol. The progressive redshift of1La relative to1Lb could easily be followed, and it was established that� =1.4 for1Lb and� = 0.5 for1La and that, with linear polarization, the OPE andTPE spectra were coincidently similar.

Two-photon resonant MPI (116) and TPE (117) of indole vapor were followedby more revealing jet-cooled TPE spectra (117). The latter contained two typesof lines, which could be assigned as1Lb and1La. The1Lb lines, such as the originand the strong 720 cm−1 line, have broad polarization-insensitive rotationalcontours and an integrated� ≈ 1.4. The1La lines have a dominant, narrowQ branch under linear polarization and a weak broad contour under circularpolarization, with integrated� ≈ 0.6–0.8. The pair of1La-type lines at 455and 480 cm−1 above the1Lb origin is a Fermi doublet involving a HT active1Lbmode (ν28), and the true1La origin lies about 1400 cm−1 above the1Lb origin,split into several components over an≈200 cm−1 range (118). The polarizedTPE of 3MI in jet (119) also showed the1La origin split, but with componentsover the range 420 cm−1 to 740 cm−1 above the1Lb origin.

One issue has been whether1La crosses1Lb upon complexation with waterwhen the water is H-bonded with theπ cloud, thereby becoming the emittingstate. Well resolved dispersed fluorescence and the finding that� = 1.25±0.05 indicate strongly that such a crossing does not occur (119a).

FLUORESCENCE ANISOTROPY—TIME-RESOLVEDSTUDIES

The first experimental verification of McClain’s (7) formalism for photoselec-tion involving three photons was by Scott et al (120), who observed both the



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steady state and time-resolved two-photon–induced fluorescence anisotropy ofbenzene in rigid 3-methylpentane at 77 K. Their results agreed with the predic-tions.

Recently, Lakowicz et al observed time-resolved two-photon fluorescenceanisotropy in fluid solutions for 2,5-diphenyloxazole (PPO) (121) and diphenyl-hexatriene (DPH) (122). The fluorescence spectra, decay times, and anisotropydecays were the same for OPE and TPE. An anisotropy (r) of 0.54 was foundfor TPE (near the theoretical maximum of 4/7), whereasr = 0.36 was foundfor OPE (near the theoretical maximum of 2/5). In contrast, the TPE-in-duced fluorescence anisotropy for indole andN-acetyl-L-tryptophanamide wasfound to be similar to or smaller than the one-photon value (123).

Prompted by the new anisotropy experiments, Callis (124) expanded therelevant portion of McClain’s (7) formalism for the purpose of demonstratinghow one- and two-photon–induced anisotropy need not be related, especiallyin aromatic systems. The possible range of two-photon anisotropy values asa function of� were found forππ∗ transitions of planar molecules. Directapplication of the formulas was made to indole and 3MI using tensors computedfrom INDO/S-CI with fair agreement with experiment. The formal analysiswas recently extended to three dimensions with no constraints (125). It wasalso found that anisotropies greater than 4/7 and less than−2/7 are apparentlypossible with TPE because of destructive interference between tensor elementsof opposite sign when there is a dominant term.

Wan & Johnson independently produced a theoretical treatment of two-photon anisotropy, which included time dependence (126, 127). In order toconveniently describe the time dependence, they used the spherical tensor basis,obtaining the same results as Callis (124) at zero time, and they applied their the-ory to TPE-induced anisotropic transient absorption in bateriorhodopsin (128).Chen & Van der Meer (129) independently derived similar expressions for thetime dependence of two-photon–induced fluorescence anisotropy that were ap-plicable to partially ordered chromophores. Andrews & Webb (130) presenteda formal symmetry analysis in irreducible tensor language of two-photon pho-toselection appropriate for either fluorescence or absorption probes, but directcomparisons with experiment were not made.

BIOPHYSICAL STUDIES

TPE studies offer an important complement to the more common fluorescenceanisotropy measurements, because� can be obtained for completely fluid solu-tions. Information is obtained under physiological conditions about absorptiononly—completely independent of subsequent solvent-solute relaxations priorto fluorescence.




Aromatic Amino AcidsPHENYLALANINE AND TYROSINE For phenylalanine (Phe) the TPE and�spectra (131) are similar to those of toluene in vapor (132, 133), solution(35, 52), and as the neat liquid (36). It is much more structured than the OPEspectrum because it is almost completely dominated by theν14 vibrationallyinduced intensity. For tyrosine (Tyr), the allowed origin is even weaker (131),because in TPE the mutuallyparaalkyl and hydroxy group perturbations can-cel instead of reinforce (13), leaving an “accidentally” forbidden origin. Thisis the reason that the TPE of tyrosinamide in water is blueshifted about 2000cm−1 from that of the OPE (131), as are the1Lb TPE bands of fluorobenzeneand pyrimidine. No vibronic structure is seen, apparently because of inho-mogeneous broadening due to the polar OH group. The result is that Pheshould be more easily detected in proteins by TPE than by OPE because ofsharper structure and because it has about the same two-photon absorptivity asTyr. (Both Tyr and Phe are similar to benzene.) The blueshifted TPE spec-trum of Tyr allows excitation with about 15-nm shorter wavelengths withoutinterference from Tyr in proteins when it is desired to excite only the tryp-tophan. This prediction was confirmed recently by Lakowicz and coworkers(134, 135).

TRYPTOPHAN The TPE and� properties for tryptophan are similar to thoseof 3MI (131), which was discussed above. Tryptophan dominates Tyr in TPEby about the same ratio as in OPE, and coincidently, there is little differencebetween the OPE and TPE spectral shapes of the1Lb-

1La band when linearlypolarized light is used. In room temperature pH 7 buffer,� levels off at avalue of about 0.52 at wavelengths>300 nm, indicative of pure1La absorption.Resolution of the TPE spectrum into1Laand1Lbcomponents was possible (131),with results similar to that found from one-photon anisotropy in propyleneglycol at−60◦C.

Nicotinamide Adenine DinucleotideSteady state and time-resolved two-photon–induced fluorescence and fluores-cence anisotropy from reduced nicotinamide mononucleotide (NAMH) and itsadenosine dinucleotide (NADH) has been reported (136). The two-photon–induced fluorescence anisotropy was 0.54 in propylene glycol at−60◦C, ingood agreement with that predicted from INDO/S-CI, which gave 0.59. Thetheory says that the two-photon tensor is dominated by the product of dipolechange and transition dipole, and the change in dipole is almost exactly paral-lel with the transition dipole. TPE of fluorescence from the related phosphate,NADPH, has been used for imaging redox processes of in situ cornea cells(137).



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Aromatic Residues in ProteinsThe first two-photon–excited fluorescence from a protein in which the fluores-cence came from an aromatic amino acid was apparently observed by Jiang andcoworkers (138–140) as early as 1983. More recently, time-resolved TPE andanisotropy studies have been applied to tryptophan and Tyr in human serumalbumin (141), purine nucleoside phosphorylases (134), Tyr in leu5-enkephalinand ribonuclease A (135), and NADH in liver alcohol dehydrogenase (136).As expected from studies on tyrosinamide (131, 134) and phenol (135), TPEaffords excitation of tryptophan at shorter wavelengths without interferencefrom Tyr. In general, the fluorescence spectra and lifetimes were found to beidentical for TPE and OPE, in contrast to some earlier reports. An exceptionwas native ribonuclease A (135), for which the fluorescence from TPE wasredshifted relative to that from OPE by 10 nm, perhaps because of the presenceof tyrosinate, which has a much stronger two-photon absorptivity than neutralTyr.

Visual Pigments and CarotenoidsTwo-photon spectroscopy has been important in the study of the visual pig-ments, retinal and its protonated Schiff base (142–146). The TPE maximumfor a modified rhodopsin containing locked 11-cis-retinal suggests that the 2“1A−g ” state lies about 2000 cm−1 above the OPA maximum, assigned to the“1B+u ” state, whereas for the isolated protonated Schiff base the two states ap-pear degenerate. The shift could be modeled only with a neutral binding site(143–145).

TPE spectra of the carotenoid region of thylakoid membranes was obtainedby monitoring chlorophyllaemission due to energy transfer from the carotenoid(147). Studies of a model carotenoid support evidence forS1–S2 mixing in vivo,with theS1(2Ag) state taking on significant oscillator strength compared to invitro (148).

NucleotidesWilliams & Callis (149) obtained polarized two-photon fluorescence excitationspectra of the four nucleotides TMP, CMP, GMP, and AMP in 0.05 M room tem-perature aqueous solutions. The two-photon absorptivities for these moleculesat 260 nm are generally about 20 times that of benzene. The results were puz-zling because the TPE spectra all have maxima that are either blue-shifted fromtheir one-photon counterparts, or in some cases show no maxima.

The�value found for the 260 nm band of TMP is 0.4, uncorrected for the nearabsence of rotational diffusion occurring prior to fluorescence (r = 0.35 forthe one-photon fluorescence anisotropy under these conditions because of the




≈2 ps lifetime) and the absence of a polarizer on the emission monochromator.This corresponds to� = 0.67 with isotropic emission and corresponds tohaving a single dominant diagonal in the two-photon tensor. This is predictedby INDO/S, because of a large dipole change nearly parallel to the transitiondipole. Thus, a TPE fluorescence anisotropy of near 4/7 is expected from TMP ina rigid medium.

Two-Photon–Induced PhotochemistryThe two-photon absorptivity for DNA was determined (149a) from the effi-ciency of cyclobutyl pyrimidine dimer formation to be about 0.5× 10−52 cm4

s/nucleotide, which is about two orders of magnitude lower than expected fromthe above study of the nucleotides (149). No explanation has been found, in spiteof considerable effort. A number of intriguing differences between one-photon–and two-photon–induced photochemistry have been reported (150–153).

OTHER SELECTED SYSTEMS

AlkanesIn an example of how TPE can be used to advantage in UV-opaque material,Orlandi and coworkers (154–156) observed fluorescence from a variety of lin-ear and cyclic alkanes using nitrogen laser excitation at 337 nm. They alsoinvestigated lifetime and energy transfer parameters. Recently, Lakowicz andcoworkers conducted similar experiments (157, 158) using 300-nm light froma doubled picosecond cavity dumped dye laser. The latter authors suggest thistechnique as a novel way to study biological membranes.

Transition Metal ComplexesMcClure and coworkers (159–163) have exploited TPE of fluorescence forassignment of d-d transitions of d3 and d6 systems in isotropic crystal fields,wherein one-photon transitions of interest are electric dipole forbidden. Bycomparing one- and two-photon spectra of PtIV in Cs2MF6 (M=Si, Ge), theone-photon spectrum was reassigned because of the particularly clear appear-ance of the A1component in the TPE spectrum (160). For Mn4+, TPE enabled anunambiguous assignment of the vibronic spectra associated with the even parityvibrational modes, revealing for the first time a strengthened Ham quenchingof spin-orbit splittings in the2T1+ ν2(eg) vibronic state (162, 163).

AminesBecause of their high fluorescence yields, TPE studies have played a role incharacterizing the lower excited states of tertiary amines (164–167). In one



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early study (165), differences in OPE and TPE spectra were traced to state-dependent depletion in the TPE due to high laser power, thereby giving insightconcerning lifetimes of different vibronic states. A recent high-resolution TPEstudy (167) of DABCO (1,4-diazabicyclo[2,2,2]octane) has provided detailedstructural information.

AcetoneTwo- and three-photon resonant MPI was used by McDiarmid & Sabljic (168)to observe and assign all three 3p← n(2py) Rydberg transitions, identifyingthe A2 (3px← n, wherex is out of plane) transition by its unique�(3) = 5/2 aswell as by its absence from OPE. Goodman and coworkers (169, 170) exploitedthese transitions in better resolved jet spectra to find the elusive a2 (in-phase)methyl torsion frequency and to assign seven of the eight a1 vibrations (171). Aphotoacoustically detected TPE study shows that the A1 (3py← 2py) transitionhas considerable valence character (172). This transition is much weaker thanthe other two in the MPI spectra but quite strong in the photoacoustic spectrum.Torsional information was also obtained for the 3s← n Rydberg transitions ofacetone (173) and acetaldehyde (174).

GlyoxalA novel and elegant study by Bickel & Innes (175) on the1Au(S1)–

1Ag(S0) tran-sition of trans-glyoxal yielded a wealth of new information on this interestingmolecule. A unique aspect of the study was tunable dye laser light shifted intothe near IR (0.7–1.4µm) by stimulated Raman shifting with high-pressure hy-drogen. One- and two-color TPE was performed by isolating one or two of theStokes lines with filters and prisms. The room temperature vapor spectra aredominated by sharp sequence bands involving one- and three-quantum changesof the HT active torsional mode,ν7.

Some other molecules for which interesting TPE studies have appearedinclude benzimidazole (114, 176), 1,4-dimethoxy-2,3-dimethylnaphthalene(177), 1,4-dimethoxy-2,3-norbornalog naphthalene (177), difluorodiazirine(178), triptycene (179), acenaphthene (53), acenaphthylene (180), and the iso-electronic series carbazole (181), dibenzofuran (182), and dibenzothiophene(183).

THEORY

GeneralA number of elegant theoretical expositions addressing generic aspects of two-photon and higher-order spectroscopies have appeared since 1979. At the mostgeneric level, Lee & Albrecht (184) have included TPA in a unified formalism




with Raman, resonance Raman, and fluorescence at the perturbation theorylevel, addressing whether a two-photon transition having an intermediate one-photon resonance is to be considered a simultaneous process, two sequentialone-photon processes, or a mixture of the two. Using a density matrix approach,they pointed out how complex line shapes result when the first photon is justoff resonance, provided pure dephasing is present, and they discussed problemswith decomposing the line shapes. TPA is also included in the Green’s functionrepresentation of second-order transition amplitudes of Singer et al (185), whohave developed new numerical methods for its application. Huo (186) presenteda “dressed molecule” approach, suitable for high intensities where perturbationtheory breaks down, and he has shown implementations using standard self-consistent field (SCF), multiconfiguration SCF (MCSCF), and configurationinteraction (CI) molecular wavefunctions.

Chen & Yeung (187) derived expressions for two-photon–induced fluores-cence in terms of irreducible tensor components of the density instead of am-plitudes, which are useful for rotationally resolved experiments. Lin et al (4),in one chapter, derive TPE rates using four different approaches: perturbationtheory, Green’s function, density matrix, and susceptibility, and they treat circu-lar/linear polarization effects at the rotationally resolved level. More relevant toexperiments reviewed in this chapter are the expressions derived by Andrews &Ghoul (188) for absorption of two, three, and four identical photons in the lan-guage of irreducible transition tensors. A useful new classification scheme wasintroduced based on the weights of the irreducible components present. Whenthe highest weight tensor is present alone, the polarization ratio�(n) = 3/2,5/2, and 35/8 forn = 2, 3, and 4, respectively. These results are in agreementwith a general result derived by Klarsfeld & Maquet (189), wherein�(n) = (2n− 1)!!/n!, [where m!! meansm(m− 2) (m− 4) . . . ]. Independently, Friedrich(190) used McClain’s formalism to determine tensor patterns and polarizationratios for three-photon excitation for many symmetry types; he also found thatfor identical photons, the maximum�(3) = 5/2. Nascimento (191) recast partof McClain’s formalism for TPA into a convenient form, but unfortunately asign error led to the incorrect conclusion that� < 1 for a number of casesinvolving transitions between states of identical symmetry.

Quantum Chemical ComputationsSemiempirical quantum calculations of two-photon spectroscopic properties ofpolyatomic systems have been quite useful. Birge and coworkers (89, 192) usedthe PPP method to predict two-photon absorptivities and polarizations for a se-ries of linear polyenes and visual pigments. At about the same time Hohlneicher& Dick (193, 194) demonstrated that CNDO/S-CI was a powerful tool for in-terpreting their extensive experimental results on aromatic hydrocarbons. Also



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at this time, Goodman and coworkers (195) demonstrated the usefulness ofINDO/S-CI for computing HT vibronic coupling effects on two-photon spectraof benzene. Common to these applications was the use of Kramers-Heisenberg-Dirac (KHD) second-order perturbation theory to evaluate the two-photon ab-sorptivity, which formally requires a sum over all intermediate states. Typically,the results converged satisfactorily after about 100–200 singly and doubly ex-cited intermediate states, provided the dipole length form of the equation wasused (193). They also found that inclusion of doubly excited configurations isnecessary to make the absolute cross sections come within an order of magni-tude of experimental values, as well as to achieve the correct ordering of statesin some cases. Otherwise, relative two-photon absorptivities and values of�

are satisfactory with only singly excited configurations. More recently, Soosand coworkers (12, 196, 197) have applied PPP with full CI to several polyenesand rings.

VIBRATIONALLY INDUCED TPA Because vibrationally induced intensity oftenis stronger than allowed intensity in the lower states of conjugated systems,computations done at fixed geometry can be misleading. Semiempirical andab initio methods have been effective at estimating relative HT TPE activity bycalculating the TPA of distorted molecules (for example 62, 195, 198, 199). Inthe case of the surprisingly strong TPA induced byν14 in the1Lb–S0 transitionof benzene, Friedrich & McClain (19) suggested that HT coupling with theground state was responsible, and they supported this idea with the observationthat the transition density matched the normal mode motions perfectly. Metz(200) argued against ground state coupling because he could show that b2uactivity exceeding that of e1u and e2u could come from E1u and E2g states ina formalism that focuses on the variation of electron repulsion integrals whenAOs are allowed to follow the nuclei during a vibrational distortion. The casewas not proven, however, because only relative intensities were computed,without showing that the ground state contribution was negligible. Mikami& Ito (201) argued more convincingly in favor of the ground state couplingon the basis of the transition density mapping and particularly on the basisof the pseudo Jahn-Teller effect, wherein the Kekule modes of benzene andnaphthalene show anomalously low frequencies in the ground state, whichincrease by∼250 cm−1 upon going to the1L−b state. They showed that 80% ofthe bond-bond polarizability stabilization of the ground state due to the Kekulemotion is contributed by the1L−b state.

Goodman and coworkers (195) also argued forcefully in favor of the1Lb–S0

coupling. They computed the b2u vibrationally induced tensor using INDO/S-CI on the distorted molecule, and showed that the variation of electron repulsionintegrals with atom separation was a small part of the mechanism, and in fact,




served to reduce the tensor elements when included. A likely source of thedisagreement lies in the use of frozen MOs and CI coefficients in the Metzanalysis (200), which may suppress important density changes. [This wasfound to be the case in a CNDO/S-CI study of vibronic coupling activity in theOPA of benzene (202).] Marconi and coworkers used CNDO/S and INDO/S CImethods to show1Lb–S0 coupling by the Kekule modes of naphthalene (198),anthracene (62), and chrysene (64). Two ab initio calculations of vibronic ac-tivity in the TPE of benzene have been reported (203, 204), both exploitingmodern response theory methods that avoid the KHD summation over interme-diate states. These techniques appear to be extremely promising, as exemplifiedby the studies by Luo et al of the TPE of benzene hot bands (204) and on the TPEspectrum of pyrimidine (109). Huo (186) has also presented a time-dependentapproach. Although, direct evidence for mixing with the ground state and1L−b is elusive because of Brillouin’s theorem, which excludes mixing betweena Hartree-Fock ground state and any singly excited configuration, recent abinitio calculations of the ground and1Lb vibrational frequencies for benzene(20, 21, 205–207) and naphthalene (205) predict a large frequency increase forthe Kekule mode, even at a modest level of theory. Goodman & Ozkabak (208)have shown that relative two-photon intensities in the hot bands ofν14 andν15provide a sensitive test of the benzene ground state ab initio force field accuracy.

In linear polyenes, the vibration corresponding toν14 of benzene is an agmode, which also alternately stretches and compresses bonds, and shares theunusual property of having a higher frequency in the 21A−g than in the groundstate. By symmetry, this mode is both FC and HT active, but the relativecontributions apparently have not been quantitatively determined. MCSCFcalculations successfully capture the frequency increases for several polyenes(209). Zgierski and coworkers (210, 211) have used the difference betweendiabatic (frozen MO and CI) and adiabatic potentials to deduce the 21A−g –S0vibronic coupling interaction.

SUBSTITUTED HYDROCARBONS Callis (199) has used CNDO/S-SCI to com-pute the relative TPA and� values for 27 benzenes and azabenzenes, singlyand multiply substituted by fluoro, methyl, amino, and hydroxy groups. Inthe same calculations, the relative contribution byν14 HT coupling was alsoobtained. The results are in good agreement with patterns predicted from per-turbation theory and pseudoparity schemes—except for the fluorine-substitutedmolecule. Judged by its effect on UV spectra, fluoro substitution is regardedas purely inductive. In experimental one-photon spectra, fluorine substitu-tion strongly enhances1L−b absorptivity but has little effect on1L+a , and doesjust the opposite in two-photon spectroscopy (10). The semiempirical resultsjust mentioned (199) disagree drastically for fluorine. Subsequent calculations



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using a longer-range electron repulsion scheme (Ohno-Klopmann instead ofMataga-Nishimoto) were found to give the correct qualitative behavior for flu-orine, without affecting the qualitative results for other substituents (211a).The 1L+a TPA for aniline and phenol was predicted to be∼10 times that ofthe benzene1L−b , as was later observed (38). Birge and coworkers (142–144)found INDO-PSDCI useful for modeling two-photon properties of perturbedpolyenes related to visual pigments. An ab initio response theory method (109)was successful at predicting the TPE spectrum of pyrimidine, accounting forrelative nπ∗ and1Lb (vibronic and allowed) intensities.

For systems that cannot be considered perturbed alternant hydrocarbons,semiempirical methods have been the sole tool for understanding and predictingTPA properties. This has been the case for indole and its derivatives (115, 124)and for nucleotides (149) whose TPA properties calculated by INDO/S-CI arein reasonable agreement with experiment.

Permanent Dipoles: The Importance of Initialand Final StatesWhether the initial and final states should be included in the summation overstates appearing in the KHD second-order perturbation theory expression for thetwo-photon tensor was decisively resolved in papers by Mortensen & Svendsen(212) and by Dick & Hohlneicher (213). The latter showed that the initial andfinal state terms alone can be large (dominant) if the transition has a large one-photon oscillator strength—and if there is a large change in permanent dipoleaccompanying the transition. Scharf & Band (214) have extended the abovetreatment to the two-color regime and have discovered that when one of the twofrequencies becomes small (<100 cm−1), that the two-photon process becomesso large as to compete favorably with the one-photon process.

Experimentally, one of the most dramatic cases where this term is dominantis for linear polyenes with polar substitution, such as the protonated Schiffbases of the retinals that are the primary visual pigments in rhodopsin andbacteriorhodopsin (144, 145). Another example of the importance of this termis for the1La transition of indoles and tryptophan (115, 124), a transition withf ≈ 0.1 and a dipole change of≈6 D. The permanent dipole term in the two-photon tensor is the reason for the low two-photon polarization,�≈ 0.5, whichallows the distinction from the overlapping1Lb–S0 transition.

SELECTED TECHNICAL ADVANCES

Detection and Cross SectionsSingle molecule detection of two-photon–excited fluorescence has been ach-ieved. Mertz et al (215) have obtained a∼100 s−1 burst rate from TPE of single




molecules in a 6 pM solution of rhodamine B, using a mode-locked Ti:sapphirelaser operating at 795 nm, 36 mW, 250 fs pulses, and 152 MHz repetition rate.Absolute two-photon cross sections have been determined over useful wave-length ranges for a number of dyes (216, 217). Xu et al (218) reported a methodfor obtaining absolute two-photon absorptivities requiring no two-photon stan-dard and no direct knowledge of the pulse time profile. The technique involvesmeasurement of the second-order autocorrelation functions using a Michelsoninterferometer. These developments can reduce problems with multi-dye scansassociated with dispersion of temporal and spatial properties of the pulses. Suchproblems were addressed in the early 1980s (52, 219, 220). Recent attention hasbeen directed to stimulated emission effects that can occur for systems whenthe TPE wavelength overlaps a broad fluorescence. Loss of signal from spon-taneously emitted light is termed light quenching (221), in itself an exploitablephenomenon (222).

Light Sources, Doppler-Free Techniques, and MicroscopyTraditional tunable dye laser sources are now partly supplanted by Ti:sapphirelasers. Raman shifting was used to extend traditional dye laser excitation to1.4-µm (175). Doppler-free TPE is possible with counter propagating beams(4, 30 ), providing resolution to∼1 MHz with a 350-mW CW system, whenthe sample is in an external resonator, which increases the intensity 30-fold.Webb and coworkers (137, 223–225) have pioneered TPE in confocal laserscanning fluorescence microscopy. Advantages of TPE for this purpose in-clude less-expensive optics, less damage to living systems, and greater depthdiscrimination because of the quadratic intensity dependence.

Higher-Order SpectroscopiesThe advent of powerful near IR sources has led to several three-photon studiesand at least one four-photon study. The three-photon excitation spectrum of the1L−b (1B2u) band of gas-phase benzene was reported by Albrecht and coworkers(226, 227). This transition is three-photon allowed by group theory, althoughpseudoparity forbidden. Remarkably, the spectrum was nearly identical to theOPE spectrum, with no trace of the origin being found. The e2g vibration,ν8,was observed for the first time in the1B2u state. The spectacular absence of theorigin line was attributed to pseudoparity, which, the authors point out, is notexpected to deny all intensity to the transition. Three-photon photoselectionand other tests rule out third harmonic generation as an artifact. The three-photon origin is seen only in strained glass (227), and in concentrated liquidsolutions (228).

Three-photon resonant MPI has been used in conjunction with the�(3) val-ues derived by Friedrich to expand and clarify the Rydberg states of benzene



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(229), hexatriene (91, 92), and acetone (168, 171). Grubb et al (230) establishedprecise first ionization potentials for benzene using (3+ 1) MPI of Rydbergstates.

Gryczynsi et al have reported the three-photon induced fluorescence andanisotropy from PPO (231) and the calcium indicator dye INDO-1 (232) usinga Ti:sapphire laser operating at 80 MHz with∼80 fs pulses in the wavelengthrange 820–890 nm. For PPOr = 0.6, which is nearly the theoretical maximumexpected for a single-diagonal element tensor. For INDO-1, excitation at 840nm gave TPE at low power density and primarily three-photon excitation athigh power density. At 885 nm, excitation was three photon, and at 820, it wastwo photon, independent of laser intensity. The three-photon signal was said tobe reasonably easy to obtain, being about ten times weaker than that from TPE.

Grubb et al (233) have observed six gerade Rydberg series as four-photonresonances in the five-photon ionization spectrum of jet-cooled benzene. Fortwo series,�(4) = 4.5± 0.5, near the theoretical value of 35/8 required forB1gandB2g states inD6h symmetry, which require at least four photons.

CONCLUSIONS AND PROSPECTS

Two-photon spectroscopy has enriched the field of electronic spectroscopymore than by simply providing alternative selection rules. It has added a newdimension by opening our minds to new concepts, such as strong vibroniccoupling between ground and excited states and the pseudoparity propensityrules. Two-photon excitation use will continue to grow in quantity, quality,and diversity, both for applied and theoretical purposes. The same may be saidmore cautiously about three-photon excitation, especially because of increaseduse of Ti:sapphire lasers. The use of circularly polarized light (measuring�) has been emphasized throughout this review as a source of valuable infor-mation concerning tensor invariants and should not be overlooked in futurestudies.

Applied uses of dyes in biological fluorescence techniques is strong mo-tivation to discover fundamental principles for understanding various classesof dyes at the two- and three-photon level. Other challenges include under-standing the surprisingly strict adherence to the pseudoparity rules by1L−b –S−0for three-photon excitation of benzene for and for one-photon excitation ofanthracene.

ACKNOWLEDGMENTS

The author thanks Professors Andy Albrecht, Lionel Goodman, and Zoltan Soosfor helpful conversations, as well as several others who sent contributions. BeritBurgess is also thanked for helping with the literature searches.




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