The fluorescence quantum yield parameter in Förster resonance energy transfer (FRET) processes underpins vital phenomena ranging from light harvesting in photosynthesis to design of sensors for monitoring physiological processes. The criteria for choosing a donor for use in FRET processes include chemical features (solubility, bioconjugatability, synthetic accessibility, and stability) as well as photophysical properties pertaining to absorption (wavelength and molar absorption coefficient) and fluorescence (wavelength and fluorescence quantum yield). The value of the donor fluorescence quantum yield (Φf, or emphatically, Φf(D)) alone has sometimes been thought (erroneously) to place a ceiling on the possible quantum yield of energy transfer (Φtrans). A high value of the donor Φf, while attractive, is not at all essential; indeed, many valuable candidates for use as FRET donors have likely been excluded on the basis of this injudiciously applied filter. Such disregard is unwarranted. In this tutorial overview, the equations for FRET are reviewed along with pertinent core concepts in photophysics. An analogy using simple hydraulics provides a pedagogical tool for the non-aficionado to better understand photochemical kinetics. Ten examples are presented of donor–acceptor systems with donors that exhibit a range of Φf values (0.60, 0.59. 0.21, 0.17, 0.12, 0.118, 0.04, 0.018, 0.007, and 0.003; i.e., 60%–0.3%), yet for each corresponding donor–acceptor pair, the value of Φtrans is at least 0.70 and in some cases nearly 1.00 (i.e., 70%–100%). The systems encompass protein, synthetic inorganic, and synthetic organic architectures. The objectives of this illustrative review are to deepen understanding of FRET and to broaden molecular design considerations by enabling selection from among a far richer set of donors for use in FRET processes.

Förster resonance energy transfer (FRET) describes the transfer of excited-state energy from one molecule to another.1–10 The FRET process occurs in many domains of science ranging from natural photosynthetic light-harvesting antenna complexes to designer molecules in bioassays and sensors. Indeed, a Web of Science search for “Förster and transfer” elicits ∼12 000 hits, whereas “FRET” elicits ∼41 000 hits. The first descriptions of intermolecular energy transfer appeared in the 1930s physical chemistry and biophysics literature concerning fluorescent dyes in solution and photosynthetic light harvesting, respectively,8 an era when core principles of photophysics and photochemistry were being conceptualized. Scientists from many walks of life outside the photophysics sanctum may have occasion to use FRET processes. Given such broad occurrence, it is not surprising that there are now nearly 20 acronyms, including FRET, to describe the energy-transfer process.11 In this tutorial overview, the term FRET will be used.

The excited-state donor molecule is invariably generated by absorption of light, and one manifestation of energy transfer is often the fluorescence emission from the acceptor. This process is illustrated schematically in Fig. 1. Over several decades, in multidisciplinary settings and as part of the PhotochemCAD initiative,12–19 a misunderstanding has often been voiced concerning the fluorescence quantum yield (Φf) of the donor in FRET. The view that “the quantum yield of energy transfer cannot be greater than the quantum yield of donor fluorescence” is erroneous and likely leads to exclusion of many prospective molecules as donors in FRET. Here, we present examples where the Φf value of the donor is very low (e.g., < 0.01, or < 1%) yet still supports a very high quantum yield of energy transfer (Φtrans > 0.70, or > 70%). This paper is aimed at addressing this issue, and in so doing, broadening the scope of molecules that can be selected as donors in FRET processes. We begin with a brief overview of the Förster process, then consider some basic concepts in the essential (albeit somewhat esoteric) field of photophysics, and finish with a handful of examples of FRET systems with high values of Φtrans despite donors with low values of Φf. The goal is not to provide a comprehensive review of the Förster process but rather to focus on the implications of the Φf parameter for molecular design of FRET systems.

FIG. 1.

Illustration of the FRET process showing the respective transition-dipole moments of donor and acceptor.

FIG. 1.

Illustration of the FRET process showing the respective transition-dipole moments of donor and acceptor.

Close modal

The perception that the yield of FRET is capped by the yield of donor fluorescence likely has multiple origins. In particular, there may be a general misperception that the Förster process occurs via the emission and reabsorption of a real photon, when instead, the process involves the transfer of a virtual photon between a closely situated donor and acceptor.20 (This concept will be expanded upon in Sec. II B.) This misperception is likely augmented by the frequently employed form of the Förster equation, which contains the Φf parameter (the fluorescence quantum yield of the donor alone) in the numerator. Regardless, the perception that the Φf value of the donor sets a ceiling on the value of Φtrans for the FRET process is erroneous. We first consider the Förster process and then turn to core concepts in photophysics.

The FRET process entails transfer of energy from the donor in the excited state to the acceptor in the ground state. The transfer process requires resonant coupling of the transition-dipole moment of the donor with the transition-dipole moment of the acceptor. The “resonant” term refers to matching the energies of the donor and acceptor excited states. The energy-transfer process can be regarded as proceeding via the coupling of two oscillators, like a weak link that joins two pendula. The magnitude of the coupling is given by the strengths of the transition-dipole moments of the donor and acceptor. For the donor, the strength is embodied in kf, the rate constant for radiative decay; for the acceptor, the strength is embodied in εA(ν), the molar absorption coefficient of the acceptor. A more comprehensive description of the FRET process is obtained from the equations given in the following. A module for carrying out FRET calculations is available as part of the PhotochemCAD program,12–14 which can make use of spectral and photophysical data for several hundred compounds.15,19

There are chiefly three equations that one encounters concerning Förster transfer. Equation (1) describes the rate constant (ktrans) for energy transfer,

ktrans(s1)=9000ln10κ2kf128π5Nn4R60fsvεAvv4dv=8.8×1023κ2kfn4R6J.
(1)

The parameter ktrans is directly proportional to kf, the rate constant for fluorescence. The parameter kf is rarely known, but can be replaced given the definition shown in Eq. (2). Hereafter, we use Φf(D) to emphasize that the parameter describes the fluorescence quantum yield of the donor in the absence of an acceptor; in other words, the donor alone in solution. Similarly, in Eq. (2) τ(D) is the excited-state lifetime of the isolated donor,

kf(s1)=Φf(D)/τ(D).
(2)

The replacement gives the well-known expression [Eq. (3)] for the rate constant of Förster energy transfer (FRET). Here, the donor fluorescence quantum yield, Φf(D), is in the numerator and is directly proportional to the rate constant for energy transfer, ktrans,

ktrans(s1)=8.8×1023κ2ΦfDn4τ(D)R6J.
(3)

The parameters in Eqs. (1)–(3) are as follows:

  • kf is the rate constant for radiative decay (fluorescence) of the donor.

  • N is Avogadro's number.

  • τ(D) is the donor singlet excited-state lifetime in the absence of an acceptor.

  • Φf(D) is the donor fluorescence quantum yield in the absence of any acceptor.

  • n is the refractive index of the medium between the donor and acceptor, not that of the bulk solvent, but typically conveniently taken as that of the bulk solvent.21 

  • R is the distance of separation (in Å) of the respective centers of the donor and acceptor transition-dipole moments.

  • κ2 is the relative orientation of the donor and acceptor transition-dipole moments.11 

  • J is the spectral overlap parameter, which describes the energy matching of the donor and acceptor excited states by the overlap of the donor fluorescence band/manifold and the acceptor absorption band/manifold.22 

  • ν is the wavenumber (cm−1) of the donor fluorescence spectrum and the acceptor absorption spectrum.

  • fs(ν) is the spectral distribution of the donor fluorescence (normalized), that is 0fs(v)dv=1.

  • εA(ν) is the molar absorption coefficient of the acceptor.

Solving Eq. (3) to obtain the value of ktrans requires knowledge of J, R, κ2, τ(D), and Φf(D). The value of J (spectral overlap) is readily obtained from knowledge of the absorption spectrum of the acceptor and the fluorescence emission spectrum of the donor. The value of R (distance) and κ2 (orientation) can be gauged from molecular models. The value of n (refractive index) can be chosen to resemble the intervening medium, such as that for a hydrocarbon solvent.

If the lifetime of the donor alone, τ(D), is available, Eq. (4) can be used to obtain the quantum yield of energy transfer,

Φtrans=ktrans1τD+ktrans.
(4)

Often, the Φf(D) for an energy donor is available whereas the value of τ(D) is not. Furthermore, in many cases, one simply wants to know the quantum yield of energy transfer, Φtrans, not the value of ktrans. To this aim, Eq. (3) is recast as Eq. (5) in terms of a center-to-center donor–acceptor distance (R0, in angstroms) for which Φtrans is 50%. At this distance (R0 = the so-called Förster distance), energy transfer is equally probable with the sum of all the other (without energy transfer) means of depopulating the excited state, which is described by the lifetime τ(D) (vide infra). In this manner, the lifetime parameter, τ(D), drops out and Eq. (5) conveniently retains only the fluorescence yield of the donor in the absence of the acceptor. The quantum yield of energy transfer (Φtrans, often referred to as T) is calculated for the actual distance (R) between donor and acceptor (centers) as shown in Eq. (6):

R06=8.8×1023κ2Φf(D)n4J,
(5)
Φtrans=R06R6+R06.
(6)

Still, the expressions for ktrans [Eq. (3)] and R0 [Eq. (5)] both have the donor fluorescence quantum yield, Φf(D), in the numerator. It is beguiling, yet incorrect, that the presence of Φf(D) in the expressions indicates that fluorescence emission is the source of energy transfer. We take up this issue in Sec. II C by considering the meaning of the Φf(D) parameter. Before turning to that issue, it is useful to consider the general process of resonance energy transfer from a more fundamental perspective.

The Förster process describes energy transfer over distances (R) that are typically less than 10 nm, which is much smaller than the 380–700 nm wavelengths (λ) of visible light. This regime corresponds to the case where the product of R and the wavevector of light, k = 2π/λ is such that k·R1. This process occurs via transfer of a virtual photon and exhibits a distance dependence of 1/R6. Resonance energy transfer can also occur over much larger distances, k·R1. In this limit, energy transfer occurs via the emission of a real photon by the donor and reabsorption of that photon by the acceptor and exhibits a distance dependence of 1/R2. These two seemingly different mechanisms are not, however, derived from independent theories. Instead, they are limiting cases of a general theory which is unified in a rigorous quantum electrodynamic (QED) treatment of resonance energy transfer.20 The QED treatment reveals that the rate constant for resonance energy transfer, ktrans(k,R), is described by

ktransk,R3+(k·R)2+(k·R)4R6.
(7)

Inspection of this equation shows that the first term in the power series dominates for the limiting case k·R1 and the 1/R6 distance dependence of the Förster process is recovered. On the other hand, the third term dominates for the limiting case k·R1 and the 1/R2 distance dependence of long-range resonance energy transfer emerges. In intermediate regimes, the full equation is necessary to describe the energy-transfer process. Finally, we note that for wavelengths of visible light, the 1/R2 dependence of resonance energy transfer is manifested at relatively short distances, on the order of a few hundred nanometers, albeit these distances are large by molecular dimensions.

The fluorescence quantum yield, Φf(D), refers to the donor fluorescence quantum yield in the absence of any acceptor. The Φf(D) parameter takes on values from 0–1 (i.e., 0%–100%). The term “quantum” arises because (1) a photon is a quantum of light, and (2) each molecule absorbs one photon. The picture of energy transfer shown in Fig. 1 concerns two molecules—a donor and an acceptor. Yet Eqs. (1)–(7) concern a collection of molecules, which is typical for almost all chemical systems in practice (except those that treat single molecules). Even a 160 μl assay vial containing 1 μM of a FRET sensor would still contain ∼1014 molecules. Herein, we focus on collections of molecules.

The fluorescence quantum yield Φf(D) can be expressed in two ways. The first is the operational expression given by Eq. (8) and the second, as the fraction of the singlet excited-state decay that occurs by fluorescence emission compared to all the decay pathways. In the absence of an acceptor, in addition to fluorescence (f) the other two singlet excited-state decay pathways are internal conversion (ic) to the ground state and intersystem crossing (isc) to the lowest triplet excited state. These three processes have rate constants kf, kic and kisc, respectively. This second definition of Φf(D) is expressed mathematically in Eq. (9),

ΦfD=numberofphotonsemittednumberofphotonsabsorbed,
(8)
ΦfD=kfkf+kic+kisc.
(9)

Typically, the fluorescence quantum yield of a (donor) sample, Φf,S, is measured using a fluorescence spectrometer to determine the intensity of the fluorescence integrated over the entire vibronic manifold (If,S) for the sample in a solution having absorbance Aλ,S at the excitation wavelength in a solvent of refractive index nS. The same is done to obtain the integrated fluorescence If,R for a reference standard with a known fluorescence yield, Φf,R in a solution with solvent refractive index nR and absorbance Aλ,R at the same excitation wavelength used for the sample. These measurements account for instrumental factors such as the wavelength dependence of the responsivity of the detection system of the fluorimeter. The target fluorescence yield Φf,S is then determined via ratio using Eq. (10),

Φf,S=Φf,RIf,S×Aλ,R×nS2If,R×Aλ,S×nR2.
(10)

The lifetime of the lowest singlet excited state of a donor chromophore in the absence of an acceptor is given by Eq. (11).23 In other words, the lifetime depends inversely on the sum of the three rate constants of the respective three pathways (fluorescence, internal conversion, and intersystem crossing) by which the singlet excited state can decay. Note that the lifetime of the excited singlet state is often referred to as the fluorescence lifetime, but the latter reflects the method of measurement; the two terms are identical. The lifetime τ(D) indicates the time for decay of the collection of excited-state molecules to reach a population with 1/e of the original number of molecules, regardless of what feature of the excited state is measured (fluorescence emission, change in absorption, emission of heat, formation of the triplet states, etc.). A typical lifetime of an excited state of an organic compound in dilute solution is several nanoseconds (ns). For example, the lifetime of chlorophyll a has been reported in the range of 5.2–7.8 ns,24 and the settled value in toluene at room temperature is 6.4 ns,25,26

τD(s)=1kf+kic+kisc.
(11)

Comparing Eq. (9) and Eq. (11) shows that the fluorescence quantum yield of the isolated donor can be recast as Eq. (12a). Similarly, the quantum yields of internal conversion and intersystem crossing are given by Eqs. (12b) and (12c), respectively. The general expression for the yield of process x (x = f, ic or isc) is given in Eq. (13):

ΦfD=kfkf+kic+kisc=kf×τ(D),
(12a)
ΦicD=kickf+kic+kisc=kic×τ(D),
(12b)
ΦiscD=kisckf+kic+kisc=kisc×τ(D),
(12c)
ΦxD=kxkf+kic+kisc=kx×τ(D).
(13)

The notions of a rate constant, quantum yield, and an excited-state lifetime are easily understood by analogy. A pool of excited-state molecules and their relaxation to the ground state can be considered akin to a tank of water emptying by several drains. Let us use chlorophyll a as an example (Fig. 2). Values for the photophysical parameters of chlorophyll a are listed in Table I.26 The photophysical parameters include the rate constants and the corresponding quantum yields.

FIG. 2.

Nature's chief absorber to capture sunlight and power the biosphere. Structure of chlorophyll a.

FIG. 2.

Nature's chief absorber to capture sunlight and power the biosphere. Structure of chlorophyll a.

Close modal
TABLE I.

Photophysical parametersa for chlorophyll a.26 

Rate constant (kx)Quantum yield (Φx)General parameters
kic = (53 ns)−1 = 1.9 × 107 s−1 Φic = 0.12 Σ kx = 1.5 × 108 s−1 
kisc = (12 ns)−1 = 8.3 × 107 s−1 Φisc = 0.55 τ = 6.4 × 10−9
kf = (19 ns)−1 = 5.3 × 107 s−1 Φf = 0.33 Σ Φx = 1 
Rate constant (kx)Quantum yield (Φx)General parameters
kic = (53 ns)−1 = 1.9 × 107 s−1 Φic = 0.12 Σ kx = 1.5 × 108 s−1 
kisc = (12 ns)−1 = 8.3 × 107 s−1 Φisc = 0.55 τ = 6.4 × 10−9
kf = (19 ns)−1 = 5.3 × 107 s−1 Φf = 0.33 Σ Φx = 1 
a

All data from samples in argon-purged toluene at room temperature.

Now, consider an idealized hydraulic analogy as shown in Fig. 3. A hydraulic tank contains 100 l of water, and can drain via three pipes of non-equal diameters. Here, the rate of draining through a given pipe depends on the diameter of the pipe. For pipes a–c of relative diameters 12 : 55 : 33, upon release of the water, the collection vessels A–C would contain 12, 55, and 33 l of water, respectively. The analogy embodies the tank of water as a collection of excited-state molecules, pipe diameter as the breadth of a channel for reaction (and disappearance) of the excited-state molecules, and the individual volumes of collected water as the respective quantum yields. The yield of volume B is simply the ratio of 55/(12 + 55 + 33), which mirrors the first equality in Eq. (12b).

FIG. 3.

Hydraulic analogy for excited-state decay via distinct channels a–c to give yields A–C, respectively.

FIG. 3.

Hydraulic analogy for excited-state decay via distinct channels a–c to give yields A–C, respectively.

Close modal

Now, consider a fictive case where an energy-transfer acceptor is positioned nearby chlorophyll, but not close enough to alter the absorption spectral properties of either the acceptor or chlorophyll. We will refer to this as a donor–acceptor complex. In this case, a new channel for depopulating the pool of excited-state chlorophyll molecules (or draining the hydraulic tank, in the analogy) has been opened up (Fig. 4). The photophysical parameters (kic, kisc, and kf) of chlorophyll remain unchanged, but the new channel is now characterized by knew. We note that any process that provides a new channel for depopulating the excited state (such as electron transfer) can be represented by this analogy; our focus here concerns excited-state energy transfer.

FIG. 4.

Hydraulic analogy for excited-state decay via distinct channels a–c plus new to give yields A–C plus NEW.

FIG. 4.

Hydraulic analogy for excited-state decay via distinct channels a–c plus new to give yields A–C plus NEW.

Close modal

The lifetime of the chlorophyll in the donor–acceptor complex is given by Eq. (14),

τDinDA(s)=1kic+kisc+kf+knew.
(14)

The quantum yield of each process (x = ic, isc, f, or new) is given simply by

Φx(DinDA)=kxkic+kisc+kf+knew=kx×τ(DinDA).
(15)

Consider the case where the ratio of the channels is 12 : 55 : 33 : 100 corresponding to kic, kisc, kf, and knew, respectively. The yield in the NEW container is 100/200 by Eq. (15), which is 50%. If the misperception stated above was in force–that the quantum yield of energy transfer (here represented by NEW) could not be greater than the fluorescence quantum yield Φf –then the quantum yield of energy transfer would have a ceiling of 33%. The yield of NEW occurs at the competitive expense of the channels for internal conversion, intersystem crossing, and fluorescence. The quantum yields for internal conversion, intersystem crossing, and fluorescence have been diminished commensurably in the donor–acceptor complex vs those for chlorophyll alone. How much? By a factor of ½ given the fact that the “new” channel is ½ of the total. In other words, the yields have been diminished from 12% to 6% for internal conversion, from 55% to 27.5% for intersystem crossing, and from 33% to 16.5% for fluorescence.

The constancy of the factors here points to another equation in photophysics known as the yield–lifetime relationship [Eq. (16)]. Given that the fundamental photophysical parameters are unchanged by introduction of a new channel for depopulating the singlet excited state, the fluorescence quantum yield Φf(D in DA) and lifetime τ(D in DA) of the donor in the donor–acceptor complex decrease commensurably,

Φf(D)Φf(DinDA)=τ(D)τ(DinDA).
(16)

As shown in Eq. (17a), the quantum yield of energy transfer, Φtrans, is obtained by knowing the excited-state lifetime of the donor alone, τ(D), and the lifetime of the donor in the donor–acceptor complex, τ(D in DA). Similarly, Eq. (17b) shows that the quantum yield of energy transfer is obtained by knowing the fluorescence quantum yield of the donor alone (Φf(D)) and the fluorescence quantum yield of the donor in the donor–acceptor complex, Φf(D in DA). And finally, the rate constant for energy transfer (ktrans) can be assessed experimentally in several ways. One mechanism is by measuring the excited-state lifetime of the donor alone and the lifetime of the donor in the donor–acceptor complex [Eq. (18a)]. Other means include knowing the fluorescence quantum yield of the donor alone and the fluorescence quantum yield of the donor in the donor–acceptor complex and either the excited-state lifetime of the donor alone [Eq. (18b)] or the lifetime of donor in the donor–acceptor complex [Eq. (18c)]. The measured rate constant can be compared with the calculated rate constant ktrans shown in Eq. (3). In all cases [Eqs. (17) and (18)], the assumption remains that all shortening of the lifetime (as reflected in the diminution of the fluorescence quantum yield) stems from the energy-transfer process with no changes in the rate constants for the competitive inherent processes (fluorescence, internal conversion, and intersystem crossing). If other competing processes (such as electron transfer) were to occur, the equations would need to be modified accordingly

Φtrans=1τ(DinDA)τ(D),
(17a)
Φtrans=1Φf(DinDA)Φf(D),
(17b)
ktrans(s1)=1τ(DinDA)1τD,
(18a)
ktrans(s1)=Φf(D)ΦfDinDA×τ(D)1τ(D),
(18b)
ktrans(s1)=1τ(DinDA)Φf(DinDA)ΦfD×τ(DinDA).
(18c)

In summary, the quantum yield of energy transfer can far exceed that of the fluorescence quantum yield, Φf(D), of the donor alone. Understanding that Φf(D) does not set a ceiling for energy transfer requires recognition that the fluorescence of the donor alone is not a dedicated process that itself alone can contribute to energy transfer. Each and every excited-state molecule in the pool can, in principle, undergo energy transfer; and the number that ultimately does transfer energy reflects competition among the various decay pathways available to all of the excited-state molecules. Yields reflect competitive kinetic processes. In FRET, the energy transfer is a new process that competes with the ordinary pathways for depopulating the excited state, namely internal conversion, intersystem crossing, and fluorescence. Depopulating a pool of excited-state molecules equates to draining the hydraulic tank in the analogy here. The introduction of a new channel of excited-state decay competes with all other (prior) channels. The hydraulic analogy presented here is not restricted to FRET processes but can be applied broadly in photophysics as well as kinetics in general. Hydraulic analogies are widely used to describe fluxes in electrical circuits and in physiology. One of the authors saw the hydraulic analogy presented in a course many years ago but is unaware of literature references concerning photophysics.

There are numerous examples where the FRET donor has a low fluorescence quantum yield yet still affords a high quantum yield of energy transfer. The following examples are believed to chiefly entail through-space (i.e., Förster) energy transfer but the parallel contribution of a through-bond process cannot be excluded. Regardless, the thrust here concerns demonstrations of a high quantum yield of energy transfer despite a weakly fluorescent donor.

The following constructs comprise a donor and acceptor joined via a covalent linker to form a donor–acceptor pair, which often is referred to as a donor–acceptor dyad, or merely a dyad. Each dyad exemplified here exhibits an absorption spectrum that closely approximates the sum of the spectra of the constituent donor and acceptor. The fluorescence spectrum of the dyad, however, shows greatly diminished fluorescence of the donor, as expected when energy transfer is a competitive process. In each case, the spectra displayed have been reproduced from the original literature. The observation of diminished fluorescence from the donor in the dyad vs the donor alone, and accompanying fluorescence from the acceptor, together support the interpretation of energy transfer from donor to acceptor.

  1. Donor Φf(D) = 0.60. The utility of FRET in the life sciences was accentuated by Stryer and Haugland,27 who showed that molecular distances could be assessed given knowledge about the quantum yield of energy transfer from a donor to an acceptor.28 The demonstration vehicle for this study was an oligo-proline scaffold bearing a naphthyl donor (D1) and a dansyl acceptor (A1) (Fig. 5). The naphthyl unit alone has Φf(D) = 0.60, whereas the value of Φtrans for the donor–acceptor pair DA-1(n) where n = 1 is 1.00 (100%). All distances for n = 1–7 gave values of Φtrans > 0.60 (>60%).

  2. Donor Φf(D) = 0.59. Another type of example arises with use of proteins with embedded visible absorbing chromophores, so-called “fluorescent proteins.” For example, a yellow fluorescent protein (YFP) as a donor (D2) exhibits Φf(D) = 0.59 (Fig. 6). The YFP was fused with a protein that contains a receptor for cyclic adenosine monophosphate (cAMP). A cyanine dye (DY-547) as acceptor A2 was tethered covalently to a cAMP unit. The cAMP-cyanine dye then binds non-covalently to the cAMP receptor site to give the resulting dyad DA-2. The dyad DA-2 exhibits Φtrans = 75%.29 

  3. Donor Φf(D) = 0.21. Many energy-transfer constructs employ chromophores that absorb and emit in the ultraviolet or visible region. In Fig. 7, a dyad is composed of pyropheophorbide a (D3) and a π-extended aza-boron-dipyrrin chromophore (aza-BODIPY, A3).30 The pyropheophorbide a is derived from chlorophyll a, whereas the π-extended aza-BODIPY is fully synthetic.31 The pyropheophorbide aabs = 668 nm) and aza-BODIPY (λabs = 737 nm) absorb in the red and near-infrared region, respectively. Pyropheophorbide a (D3) alone has Φf(D) = 0.21.19 Illumination of the dyad DA-3 (in benzene) at 410 nm, which selectively excites the pyropheophorbide moiety, results in energy transfer from the pyropheophorbide a to the aza-BODIPY with quantum yield Φtrans > 0.95 (>95%).30 

  4. Donor Φf(D) = 0.17. Most of the constructs considered here contain chromophores that yield π–π* excited states. An example of a construct (DA-4) with metal-ligand charge-transfer states is provided in Fig. 8.32 The rhenium(bipyridyl)(CO)3 chromophore (D4) is the donor and the chromium(pyridyl-acac)3 chromophore is the acceptor. A chromium(phenyl-acac)3 chromophore (A4′) is used as a surrogate for the acceptor. The rhenium(bipyridyl)(CO)3 chromophore has Φf(D) = 0.17. Here, the emission is from a multiplet state, not a singlet state, but for consistency we employ the fluorescence terminology. The lifetime is τ ∼ 600 ns, as measured in a surrogate (D4′) analogous to DA-4 wherein Cr(III) is replaced with Ga(III) so that energy transfer does not occur. In DA-4, the rate constant for energy transfer (1.7 × 108 s−1) competes very favorably with the donor lifetime, affording Φtrans ∼ 0.99. Here, the presence of three donors provides enhanced absorption but only one is excited at a given time under typical low light intensity.

  5. Donor Φf(D) = 0.12. In a dyad composed of a porphyrin and a cyanine dye, DA-5, the porphyrin (D5) is the donor, and the heptamethine cyanine dye (A5) is the acceptor (Fig. 9).33 The porphyrin constituent, D5, exhibits Φf(D) = 0.12, which was determined on the basis of the standard value in that era (Φf(D) = 0.11)34,35 for the benchmark meso-tetraphenylporphyrin. Illumination at 417 nm, where the porphyrin absorbs preferentially, causes diminution of the porphyrin fluorescence (Φf(D in DA) ∼ 0.011), as expected in the case for introduction of the competing process of energy transfer. Emission occurs almost entirely from the cyanine dye. Here, the quantum yield of energy transfer (Φtrans) from porphyrin to cyanine is 0.91 (91%).33 

  6. Donor Φf(D) = 0.118. FRET is widely employed in the life sciences to gauge molecular proximity, both to determine distances in biomolecules (i.e., a spectroscopic ruler) and as part of bioassays. In many cases, the donor is a tryptophan (Φf(D) = 0.118) in a protein. One example concerns energy transfer from tryptophan to a bound drug analogue in human serum albumin (HSA).36 Here, the bound species is an analogue of warfarin, namely, (E)-7-hydroxy-3-(3-(2,3-dimethoxyphenyl)-acryloyl)-2H-chromen-2-one (A6), and the donor is tryptophan (D6) at position 214 in HSA (Fig. 10). The quantum yield of energy transfer from Trp214 to the chromene in DA-6 is Φtrans = 0.74.

    The use of FRET in the life sciences is vast. We note, however, that in many cases studied, the distances are greater than the so-called Förster distance (R0), the distance at which the yield of energy transfer is 50%. In such cases, although the Φf(D) of the donor alone may be quite low, as in the case for tryptophan, the large distance inevitably causes the value of Φtrans to also be low. For example, several acceptor chromophores were covalently attached to a cysteine thiol in DNA polymerase III holoenzyme. The transfer of energy from the tryptophan (Φf(D) stated to be 0.13 in this report) to attached stilbene, pyrene, or fluorescein proceeded with Φtrans values of 0.34, 0.65, or 0.58, respectively.37 

  7. Donor Φf(D) = 0.040. In a dyad (DA-7) composed of two oxochlorins, the zinc oxochlorin (D7) is the donor and the free base oxochlorin (A7) is the acceptor (Fig. 11). The zinc oxochlorin D7 alone has Φf(D) = 0.040 (i.e., 4.0%) and τ = 700 ps. Yet, in the dyad DA-7, the lifetime of the excited zinc oxochlorin is 120 ps. The quantum yield of energy transfer from zinc oxochlorin to the free base oxochlorin is 0.80 (80%).38 

  8. Donor Φf(D) = 0.012. A coumarin–fullerene dyad (DA-8) is shown in Fig. 12. The coumarin D8 is the donor and alone has Φf(D) = 0.012.39 The fullerene (A8) serves as the acceptor. Illumination of the dyad (in toluene) at 300 nm, which selectively excites the coumarin moiety, results in energy transfer from the coumarin to the fullerene. The quantum yield of energy transfer Φtrans is 0.92 (92%).39 

  9. Donor Φf(D) = 0.007. A donor–acceptor architecture (DA-9) was prepared by self-assembly given the affinity of free base dipyrrins for coordination of a zinc ion to give a bis(dipyrrinato)zinc(II) unit (Fig. 13).40 The construct DA-9 contains one bis(dipyrrinato)zinc(II) unit as the donor and two identical zinc porphyrins as the acceptors. The bis(dipyrrinato)zinc(II) unit D9 alone in toluene exhibits Φf(D) = 0.007 (0.7%), yet the quantum yield of energy transfer of DA-9 is 0.97 (97%). The high yield accrues because, as in the prior examples, the rate constant for energy transfer is greater than the sum of those for the other pathways for depopulating the singlet excited state. More in depth, the lifetime of the donor D9 alone is 93 ps. On the other hand, in the triad, the lifetime of the donor D9 unit is only 1.4 ps. Thus, the rate constant for energy transfer from the donor unit (resembling D9) to a zinc porphyrin unit (resembling A9) is ktrans = (2 × 1.4 ps)−1 − (93 ps)−1 = (2.8 ps)−1; the quantum yield Φtrans = [1 − 2 (1.4 ps)/(93 ps)] = 0.97. Here, the factor of 2 enters because there are two acceptors rather than one, and transfer can occur with equal probability to either one. The presence of two acceptors does not alter the fundamental FRET considerations other than that there are two equivalent pathways for depopulating the excited state of the donor rather than one, as is the typical case for a donor–acceptor pair.

     The bis(dipyrrinato)metal complexes were first discovered by the estimable Hans Fischer nearly 100 years ago, in 1924.40–42 Such compounds were anecdotally regarded over the years as “non-fluorescent.” The utility of such complexes as energy-transfer donors was apparently not considered. There is a fundamental distinction between “not fluorescent” and “only weakly fluorescent.” The bis(dipyrrinato)zinc(II) complex D9 falls into the latter category. The results for the bis(dipyrrinato)zinc–porphyrin triad accentuate the point that weakly fluorescent molecules can be excellent donors in energy-transfer processes. In the triad DA-9, the bis(dipyrrinato)zinc(II) unit forms a self-assembling linker to join the two porphyrins, captures light in the blue-green region, and transfers excited-state energy with high quantum yield to the neighboring porphyrins.40 Few other chromophores provide all three features. Many other chromophores that exhibit weak fluorescence (a proxy for a short excited-state lifetime) may be suitable for use in FRET processes, and in conjunction with other molecular attributes, may offer distinct and as-yet unexplored phenomena.

FIG. 5.

Naphthyl–dansyl dyads DA-1(n) and constituents D1 and A1 are shown at the top. (A) The absorption spectra (solid lines) of the donor D1 (blue) and acceptor A1 (red) are shown along with the fluorescence spectra (dashed lines) of the donor D1 (blue) and acceptor A1 (red). (The same format is employed in all subsequent figures.) (B) The yield of energy transfer obeys a 1/R6 dependency as shown by the change in the number n of proline units in the spacer.27 

FIG. 5.

Naphthyl–dansyl dyads DA-1(n) and constituents D1 and A1 are shown at the top. (A) The absorption spectra (solid lines) of the donor D1 (blue) and acceptor A1 (red) are shown along with the fluorescence spectra (dashed lines) of the donor D1 (blue) and acceptor A1 (red). (The same format is employed in all subsequent figures.) (B) The yield of energy transfer obeys a 1/R6 dependency as shown by the change in the number n of proline units in the spacer.27 

Close modal
FIG. 6.

A yellow fluorescent protein (YFP) fused with a cyclic adenosine monophosphate (cAMP) receptor protein (D2, upper left) complements a cyanine dye tethered to a cAMP unit (A2, upper right). Binding of D2 and A2 results in energy transfer, illustrated at lower left. The absorption spectra (solid lines) of the donor D2 (blue) and acceptor A2 (red) are shown at right, along with the fluorescence spectra (dashed lines) of the donor D2 (blue) and acceptor A2 (red).29 

FIG. 6.

A yellow fluorescent protein (YFP) fused with a cyclic adenosine monophosphate (cAMP) receptor protein (D2, upper left) complements a cyanine dye tethered to a cAMP unit (A2, upper right). Binding of D2 and A2 results in energy transfer, illustrated at lower left. The absorption spectra (solid lines) of the donor D2 (blue) and acceptor A2 (red) are shown at right, along with the fluorescence spectra (dashed lines) of the donor D2 (blue) and acceptor A2 (red).29 

Close modal
FIG. 7.

A pyropheophorbide a – aza-BODIPY dyad (DA-3), the pyropheophorbide a donor (D3), and the aza-BODIPY acceptor (A3) are shown at the top.30 (A) The absorption spectra of the donor (D3, blue line) and the acceptor (A3, red line) are shown along with the fluorescence emission of the aza-BODIPY (A3, dashed red line) and the pyropheophorbide a donor D3 (dashed blue line). (B) The absorption spectrum of dyad DA-3 (solid black line at lower right) closely resembles the sum of the spectra of D3 (blue line in panel A) and A3 (red line in panel A). The fluorescence emission of dyad DA-3 (dashed black line) closely resembles that of the aza-BODIPY (A3, dashed red line in panel A) with very little contribution from the pyropheophorbide a donor D3 (dashed blue line in panel A), commensurate with a high quantum yield of energy transfer from donor to acceptor.

FIG. 7.

A pyropheophorbide a – aza-BODIPY dyad (DA-3), the pyropheophorbide a donor (D3), and the aza-BODIPY acceptor (A3) are shown at the top.30 (A) The absorption spectra of the donor (D3, blue line) and the acceptor (A3, red line) are shown along with the fluorescence emission of the aza-BODIPY (A3, dashed red line) and the pyropheophorbide a donor D3 (dashed blue line). (B) The absorption spectrum of dyad DA-3 (solid black line at lower right) closely resembles the sum of the spectra of D3 (blue line in panel A) and A3 (red line in panel A). The fluorescence emission of dyad DA-3 (dashed black line) closely resembles that of the aza-BODIPY (A3, dashed red line in panel A) with very little contribution from the pyropheophorbide a donor D3 (dashed blue line in panel A), commensurate with a high quantum yield of energy transfer from donor to acceptor.

Close modal
FIG. 8.

A rhenium(bipyridyl) (CO)3 chromophore (D4) is the donor and the chromium(pyridyl-acac)3 chromophore (A4) is the acceptor in DA-4 (shown at top).32 (A) The emission spectrum of surrogate D4′ closely overlaps the absorption spectrum of surrogate acceptor A4′. (B) The absorption spectrum of dyad DA-4. Note the different absorbance scales in panels (A) and (B).

FIG. 8.

A rhenium(bipyridyl) (CO)3 chromophore (D4) is the donor and the chromium(pyridyl-acac)3 chromophore (A4) is the acceptor in DA-4 (shown at top).32 (A) The emission spectrum of surrogate D4′ closely overlaps the absorption spectrum of surrogate acceptor A4′. (B) The absorption spectrum of dyad DA-4. Note the different absorbance scales in panels (A) and (B).

Close modal
FIG. 9.

A porphyrin–cyanine dyad (DA-5) and the constituent donor D5 and acceptor A5 are shown at the top. (A) The spectral features of the donor and acceptor constituents. (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-5.33 

FIG. 9.

A porphyrin–cyanine dyad (DA-5) and the constituent donor D5 and acceptor A5 are shown at the top. (A) The spectral features of the donor and acceptor constituents. (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-5.33 

Close modal
FIG. 10.

A drug analogue (A6) binds to a site in human serum albumin (shown at top). Reprinted with permission from Khammari et al., Phys. Chem. Chem. Phys. 19, 10099–10115 (2017). Copyright 2017 Royal Society of Chemistry (Great Britain).36 The fluorescence spectrum of D6 and the absorption spectrum of A6 are shown (lower right). Energy transfer from tryptophan at site 214 (D6) proceeds with Φtrans = 0.74.

FIG. 10.

A drug analogue (A6) binds to a site in human serum albumin (shown at top). Reprinted with permission from Khammari et al., Phys. Chem. Chem. Phys. 19, 10099–10115 (2017). Copyright 2017 Royal Society of Chemistry (Great Britain).36 The fluorescence spectrum of D6 and the absorption spectrum of A6 are shown (lower right). Energy transfer from tryptophan at site 214 (D6) proceeds with Φtrans = 0.74.

Close modal
FIG. 11.

An oxochlorin dyad (DA-7) and the constituent donor D7 and acceptor A7 are shown at the top. (A) The spectral features of the donor and acceptor constituents. (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-7.38 

FIG. 11.

An oxochlorin dyad (DA-7) and the constituent donor D7 and acceptor A7 are shown at the top. (A) The spectral features of the donor and acceptor constituents. (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-7.38 

Close modal
FIG. 12.

A coumarin–fullerene (C60) dyad (DA-8) and constituents are shown at the top. (A) The spectral features of the donor and acceptor constituents (the fluorescence spectrum of the acceptor was not available). (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-8.39 

FIG. 12.

A coumarin–fullerene (C60) dyad (DA-8) and constituents are shown at the top. (A) The spectral features of the donor and acceptor constituents (the fluorescence spectrum of the acceptor was not available). (B) The absorption spectrum (solid black line) and fluorescence spectrum (dashed black line) of DA-8.39 

Close modal
FIG. 13.

A bis(dipyrrinato)zinc–porphyrin construct (DA-9), the bis(dipyrrinato)zinc donor constituent D9, and the zinc porphyrin acceptor A9 are shown at the top. (A) The spectral features of the constituents D9 and A9. (B) The spectral features of DA-9.40 The two zinc porphyrins in DA-9 are identical and are displayed in edge-on and face-on perspectives given the orthogonal orientations of the two dipyrrin units in the bis(dipyrrinato)zinc complex.

FIG. 13.

A bis(dipyrrinato)zinc–porphyrin construct (DA-9), the bis(dipyrrinato)zinc donor constituent D9, and the zinc porphyrin acceptor A9 are shown at the top. (A) The spectral features of the constituents D9 and A9. (B) The spectral features of DA-9.40 The two zinc porphyrins in DA-9 are identical and are displayed in edge-on and face-on perspectives given the orthogonal orientations of the two dipyrrin units in the bis(dipyrrinato)zinc complex.

Close modal
  1. Donor Φf(D) = 0.003. A free base porphyrin bearing four coumarin donors (DA-10) is shown in Fig. 14.43 The energy-transfer donor is the coumarin (D10), which alone has Φf(D) = 0.003 (0.3%). The porphyrin A10 is the acceptor. The presence of four donors per acceptor does not alter the fundamental considerations for the FRET process, because at the typical low light intensity employed, only one coumarin in the construct DA-10 is excited at a given time. The only consequence of having four coumarins rather than one is that the probability of light absorption by a coumarin in DA-10 is four times greater than would be the case with a dyad composed of a single coumarin. In other words, the net molar absorption coefficient of the donor [εD(ν)] is increased by a factor of four. Note that although εD(ν) does not explicitly appear in any of the Förster equations, εD(ν) does enter via kf as reflected in the Einstein relationship (which can be implemented by the Strickler–Berg treatment for molecular spectra). The coumarin fluorescence spectrum overlaps with the porphyrin Soret band (reflecting absorption to an upper excited state) at 419 nm. Illumination of DA-10 in the ultraviolet preferentially excites the coumarin unit and affords a quantum yield of energy transfer Φtrans = 0.97 (97%).43 

FIG. 14.

A free base porphyrin bearing four coumarin donors (DA-10) and constituents are shown at the top. (A) The absorption and fluorescence spectra of the donor (D10, blue lines) and acceptor (A10, red lines). (B) The absorption and fluorescence spectra of the construct (DA-10).43 

FIG. 14.

A free base porphyrin bearing four coumarin donors (DA-10) and constituents are shown at the top. (A) The absorption and fluorescence spectra of the donor (D10, blue lines) and acceptor (A10, red lines). (B) The absorption and fluorescence spectra of the construct (DA-10).43 

Close modal

The preceeding examples show that a high quantum yield of energy transfer (Φtrans) can be achieved despite a low value of the donor fluorescence yield Φf(D). The low value reflects the ratio of kf to the sum of all rate constants (kf, kic, and kisc) as shown in Eq. (9). Still, as a point of perspective, it is germane to ask the question of the effect of an increase in the value of kf, assuming all other rate constants remain fixed, particularly on the value of ktrans. In short, the value of kf and ktrans are directly proportional: increasing the value of kf would increase the value of ktrans, all other things being equal. However, Einstein showed that kf and ε are directly related, as (spontaneous) radiative decay and (stimulated) radiative absorption are reciprocal transitions.44 This relationship is now known as the Einstein relation. Hence, it is not possible to alter the value of kf (of the donor) without simultaneously altering the intensity, and therefore likely the shape, of the lowest-energy absorption band, and by mirror image, the emission band (of the donor). In so doing, the spectral overlap parameter is likely to be altered commensurably.

Knowledge of the value of the kf parameter in the Förster expression [Eq. (1)] requires measurement of the fluorescence yield (which is routine) as well as the singlet excited-state lifetime (which has been less common in the past but has become more common over the years). Hence, a more thorough analysis of the aforementioned examples is not feasible. The kf value was determined, however, for a series of tetrapyrrole macrocycles including a porphyrin, chlorin, and bacteriochlorin, which have similar molecular frameworks but differ in the nature of the π-chromophore. The porphyrin (P1),45 chlorin (C1),45 and bacteriochlorin (B1)46 were equipped with polyethylene glycol (PEG) chains to support solubilization in water, and the photophysical properties were recorded in water and in the organic solvent N,N-dimethylformamide (DMF) (Fig. 15). The value of the kf parameter increases in the series of the porphyrin [(180 ns)−1 = 5.6 × 106 s−1], chlorin [(41 ns)−1 = 2.4 × 107 s−1], and bacteriochlorin [(16 ns)−1 = 6.3 × 107 s−1],45 reflecting increased absorption intensity of the long-wavelength transition and the reciprocal relation via Einstein of the absorption intensity and the kf parameter. Here, profound electronic changes arise—the porphyrin absorbs weakly in the red, the chlorin absorbs moderately in the red, and the bacteriochlorin absorbs strongly in the near-infrared spectral regions—the value of kf only changes over a factor of 11-fold, yet the value of Φf changes only by a factor of ∼3-fold. The photophysical parameters recorded in DMF are listed in Table II.45 The more pronounced changes occur in the values of the rate constant for internal conversion (kic, 66-fold) and the yield of internal conversion (Φic, 16-fold).

FIG. 15.

Porphyrin (P1), chlorin (C1), and bacteriochlorin (B1) compounds for comparative photophysical studies.

FIG. 15.

Porphyrin (P1), chlorin (C1), and bacteriochlorin (B1) compounds for comparative photophysical studies.

Close modal
TABLE II.

Photophysical properties of porphyrins, chlorins, and bacteriochlorins.a

Compoundτs (ns)ФfФiscФickf−1 (ns)kisc−1 (ns)kic−1 (ns)
P1 14.0 0.077 0.90 0.023 180 16 600 
C1 10.2 0.25 0.63 0.12 41 16 85 
B1 3.20 0.20 0.42 0.38 16 
Compoundτs (ns)ФfФiscФickf−1 (ns)kisc−1 (ns)kic−1 (ns)
P1 14.0 0.077 0.90 0.023 180 16 600 
C1 10.2 0.25 0.63 0.12 41 16 85 
B1 3.20 0.20 0.42 0.38 16 
a

All data are for samples in DMF at room temperature. The typical errors (percent of value) of the photophysical properties are as follows: τS (±7%), Φf (±5%), Φisc (±15%), Φic (±20%), kf (±10%), kisc (±20%), and kic (±25%).45 

For compounds that have a low Φf(D) value, the generally better strategy to increase the Φf(D) value may be to focus on diminishing the value of kic or of kisc, if possible, rather than increasing the value of kf, although no such strategies may be available. As a general rule, there is no magic molecular knob that can be turned to increase the value of kf. The concept of slowing internal conversion by suppressing internal motions is well known and will not be repeated here. Indeed, G. N. Lewis and M. Calvin referred in 1939 to rotatable molecular entities as “loose bolts,”47 an era when Kasha had just begun the experimental work48 that would lead to formulation of one of the basic principles of photochemistry, Kasha's rule.49 A beautiful historical account of this era is available.50 While such concepts were enunciated three quarters of a century ago, the development of molecular design and synthesis strategies that capitalize therefrom remains a fertile area of ongoing research.51–54 Ultimately, the adverse impact of a low Φf(D) value of a prospective donor in a donor–acceptor construct can be overcome in many cases by bringing the donor and acceptor close enough such that the value of ktrans greatly exceeds the sum of the other rate constants for the donor alone, 1/τ(D), in which case energy transfer becomes the dominant process for depopulating the collection of excited-state donor molecules. The examples outlined above do just that.

The donor and acceptors in a FRET process are typically chosen on the basis of distinct criteria. In a bioassay sensor, for example, ideally the donor is chosen for absorption spectral properties (λexc and εexc) whereas the acceptor is chosen for fluorescence spectral properties (λem and Φf). Indeed, one advantage of a FRET process is the ability to separately choose the properties of the emitter (donor) and absorber (acceptor). One parameter that has been seemingly overemphasized, however, is the Φf(D) of the donor. While a high value for the Φf(D) of the donor is beneficial, it does not follow that a donor with a low value for Φf(D) is a poor candidate. The fluorescence quantum yield of the donor in FRET does not present an intrinsic ceiling on the possible quantum yield of energy transfer.

The issues raised herein have come to the fore during the course of development of PhotochemCAD12–19 and also in our parallel research concerning synthetic arrays for fundamental studies of light-harvesting and charge-transfer phenomena.55 The misperception outlined here—that the fluorescence of the donor is the only channel that can give rise to energy transfer—has likely caused many potential chromophores to be relegated to the “unsuitable” category upon consideration as FRET donors. Many compounds exhibit modest, weak or seemingly negligible fluorescence and have undoubtedly been the recipient of “misguided disregard.”17 Many Φf(D) values are likely not reported because a low value elicits the perception of little utility in the photosciences. Others are reported with a surprising range of values in the literature.35 While there are many design choices that enter in selection of a donor and acceptor in a FRET-based biosensor56 or light-harvesting architecture, a low value of the fluorescence quantum yield should not be a prima facie basis for rejection as a donor in a FRET process.

This work was supported by Grant No. DE-FG02-05ER15661 from the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, of the U. S. Department of Energy.

There are no conflicts to declare.

The data that support the findings of this study are available within the article.

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