Light absorption-fate of the excited state, Chemistry tutorial

Introduction

Photochemistry is the study of what occurs to molecules when they absorb light. Thus it is significant to believe the features affecting whether and how proficiently molecules absorb. In addition, in the extremely short time-frame after a molecule has absorbed light; it can undergo a diversity of procedures. In applications, we might desire a exacting process, so once more an understanding of what pathways are accessible to excited states is significant so that systems can be optimized as needed (for example via changing solvent, modifying the molecule).

Electronic excited states are thermodynamically unstable. They persevere for lifetimes that are usually about 10 nanoseconds for many medium sized organic molecules. A number of evolution metal complexes have lifetimes of about 1 microsecond. Triplet states, resulting from a spin inter-conversion procedure in the excited state, contain fairly long lifetimes, sometimes to beyond 1 millisecond.

Closed shell organic species, which are electrically neutral always, have single electronic ground states; electronic selection rules need that absorption of light can take place only when the electronic spin multiplicity is unchanged during the transition. Though, molecular vibrations and interactions between neighbouring molecules give methods for molecules to jump between electronic energy levels either through the similar or dissimilar spin multiplicity. As molecules relax from excited states, they can proceed along many dissimilar mechanistic pathways. An easy fate of an excited state molecule is to release fluorescence. Fluorescence is the light emission that happens from the v' = 0 excited electronic state back down to the ground electronic state. Spontaneous emission is the normal fluorescence that happens by a random probability. Stimulated release is the reverse of a (stimulated) absorption evolution, where a photon of exactly the accurate wavelength and direction comes along and knocks the excited state down to the ground state, taking through it a 2nd identical photon. LASERs (Light Amplification via Stimulated Emission of Radiation) function when an excited state attains a population inversion, and all of the photons released from the gain medium have the similar characteristics. Lasers misbehave, or cease to function when stimulated release starts to lose the rate competition against spontaneous emission.

Light Absorption - Formation of the Excited State

Photochemistry is depends on the reaction/reactivity of molecules in their excited state after they contain absorbed light. By 'light', we indicate that part of the electromagnetic spectrum that can promote electrons in the outer atomic orbitals to unoccupied orbitals - for instance electrons near or at the elevated occupied molecular orbital (HOMO) to orbitals near or involving the lowest unoccupied molecular orbital (LUMO). To do this, the light must be of adequate energy to promote electrons between electronic energy levels, and this is originate to be light in the UV/visible region of the electromagnetic spectrum. For this cause, the region of the spectrum 200 nm < λ < 800 nm is sometimes termed to as the 'photochemical window'. The range of wavelengths in the spectrum and the consequence of absorption via the atom/molecule are exposed below.

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Figure: Regions of the electromagnetic spectrum and their impact on atom structure

Therefore, absorption of a photon of light of wavelength 200 - 800 nm might consequence in a HOMO-LUMO evolution. An extremely clear indication of this is examined in d-block complexes. For example, a ruthenium (II) complex has 6 d-electrons and has a low spin octahedral configuration t2g6. On absorption of visible light (λ ~450 nm), an electron is promoted to an eg orbital, giving the compound its red-orange colour. This transition is in the visible region. For d0 complexes such as TiO2, a d-d transition is not possible, and a transition from the oxide ligand to the metal centre - a ligand - to metal charge transfer (LMCT) transition happens, but only if the molecule is irradiated via UV light (λ < 390 nm). Hence TiO2 is white, as it doesn't absorb any visible light.

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Figure: Absorption of a photon of visible light causes a d-d transition in Ru(II) giving the molecule a visible colour.

Excited electronic states carry vibrational and rotational excitation immediately after their creation.

Though absorption of light most frequently happens from ground electronic states for that the vibrational quantum number is v = 0, the rotational quantum number  J  is zero only for incredibly cold, isolated molecules (these as those prepared in a gas-phase supersonic free jet expansion, or kept in a liquid helium cryostat for condensed phase samples). Though, the Franck-Condon principle illustrates that we can access a number of excited vibrational states during the electronic transition.

The Franck-Condon Principle  

The principle states that the absorption of a photon is an almost instantaneous procedure, because it engages only the rearrangement of practically inertia-free electrons. During light absorption, which occurs in femtoseconds (10-15s), electrons can shift, not the nuclei. The much heavier atomic nuclei have no time to readjust themselves during the absorption perform but have to do so after it is over, and this readjustment swings them into vibration. Excitation according to Franck-Condon principle isn't to the lowest vibrational level (analogous to a non-vibrational state), but somewhere higher (Franck-Condon state), and the transition engaged, a vertical transition (Figure). This stands for that the molecule discovers itself, after the absorption act, in a non-equilibrium state and starts to vibrate like a spring. The periods of these vibrations are of the order of 10-13 sec. Since the common lifetimes of excited electronic states are of the order 10-9 sec, there is sufficient time during the excitation period for many thousands of vibrations. During this period, equilibrium can be established through a non-radiative relaxation to the non-vibrational v0 state.

A catalogue of several important photo physical processes.

Photo-induced excited states are generated via absorption or scattering of one or more photons. Scattering and multi-photon procedures need the intense light fields available only from lasers. Multi-photon and light scattering processes are said nonlinear optical phenomena, since unlike stimulated absorption; they don't base linearly on the excitation intensity (or power). Several of the most significant excited state relaxation processes are listed below:

  • Fluorescence (stimulated and spontaneous emission)
  • Intersystem Crossing (jumps between electronic excited state manifolds of dissimilar spin multiplicity)
  • Internal Conversion (downward energy jump from higher to lower lying excited states having the similar spin multiplicity)
  • Phosphorescence (lower energy spontaneous release occurring from longer-lived excited states, usually triplet multiplicity)
  • Energy Transfer (excitation convey, or exciton annihilation-photosynthetic antenna proteins, diode lasers)
  • Photochemical Reactions (photosynthesis, photo-induced electron-transfer, photo- dissociation).
  • Excited State Solvatochromism (relaxation of molecular excited state reasoned via strong electric interactions through solvent)

The photo physical procedures fluorescence, vibrational relaxation, internal conversion, intersystem crossing, and phosphorescence are demonstrated schematically in the diagram below. In the colored diagram above, three electronic states for a diatomic molecule are symbolized by the Morse potential curves. The ground electronic state S0 is a single (paired spin, or filled shell) configuration, characteristic of most neutral organic molecules. The 1st single excited state, S1, is coloured blue. The lowest energy unpaired-spin configuration is a triplet state tagged T1, exposed at top right as the dark green curve.

 

1409_The photophysical processes fluorescence, vibrational relaxation, internal conversion.jpg

Figure: The photo physical processes fluorescence, vibrational relaxation, internal conversion, intersystem crossing, and phosphorescence.

Each of the three Morse potential curves has the 1st numerous vibrational levels exposed explicitly. Rotational levels are much more densely spaced, and though quite significant, aren't exposed.

The Jablonski diagram

2396_A Jablonksi diagram for an organic molecule..jpg

Figure: A Jablonksi diagram for an organic molecule. 

Radiative processes (those which are 'vertical' in energy transfer) are exposed in solid lines whereas non-radiative processes ("horizontal" energy transfer) are revealed using dotted lines. Indicative timescales are exposed, even though are molecule-dependant. In principle the Jablonski diagram is similar to the evolutions in the potential energy curves, exposed above, except the potential energy curves are generally not symbolized. An easy Jablonski diagram for an organic molecule is shown above. As we know that a similar diagram for an inorganic compound will as well comprise metal orbitals, so will be dissimilar in style. 

Photo-excitation by Stimulated Absorption

Photo-excitation can induce a stimulated absorption transition from S0 to S1 indicated in Figure 2 by the vertical energy jump labelled hν, connecting the S0, v=0 state to the S1, v=3 state. The vertical Franck-Condon transition in energy occurs nearly instantaneously, without the atomic nuclei being able to respond yet. One can think of the relevant time scales for the vertical energy transition as follows: The transition is will likely occur within one period T=1/ν of the optical cycle. If we consider that typical wavelengths for electronic transitions for diatomic molecules are in the ultraviolet, an estimate for a UV wavelength of 300 nm (3 x 10-7 m) and the speed of light c (3 x 108 m/s) corresponds to a frequency ν = 1015 Hz, or 1 PetaHertz. The period T is then 10-15 seconds, or one femtosecond.

Immediately following the transition, the diatomic molecule now resides on the potential energy curve (surface, for a polyatomic molecule) through the geometry of the ground state, and starts to vibrate through traits of the excited state v=3 level. Note that the blue S1 potential energy curve is broader than the dark red S0 curve. For this case, it means that the excited state trait vibrational frequency will be lower than in the ground state.

Vibrational Relaxation

A specified vibronic excited state for a diatomic molecule these as the S1, v=3 state exposed above might be stable for nanoseconds to even one second, depending on atmosphere and temperature. Though, the common case for polyatomic molecules is in common extremely dissimilar. For medium and larger sized molecules (10 or more atoms), the density of the numerous vibrational potential energy curves leads to a multi-dimensional excited-state potential energy surface that is densely packed by both vibrational and rotational levels. The black diagonal arrows specify the direction of the relaxation procedure in normal organic molecules: the S1,v=3 state will relax rapidly to the S1,v=2 state, followed by subsequent relaxation to the S1,v=1 and S1,v=0 vibronic levels. The larger the molecule, the more quick the relaxation can become. For a molecule these as an amino acid, a tetrapyrrole (such as chlorophyll a, or a heme), and the vibrational population relaxation can be complete in < 25 femtoseconds. In addition to intramolecular pathways made possible by the coupling between an elevated density of anharmonic states, contacts through neighbouring molecules (gas-phase collisions, or low-frequency collective vibrations in liquids or phonons in solids) as well enhance the rate of vibrational relaxation. While much has been learned both theoretically and experimentally about the vibrational relaxation processes, there is no quantitative theory that can predict the vibrational relaxation a priori.

Radiative versus Non-Radiative Excited State Decay Pathways

After vibrational relaxation has occurred over the time scale of several tens of femtoseconds to many picoseconds, the molecule will be metastable in the S1,v=0 state for a time frame ranging from hundreds of picoseconds (10-10 s) to hundreds of nanoseconds (10-7 s). From the S1,v=0 level, the ultimate relaxation to the ground state can proceed via 2 common pathways: one radiative, in that light is released from the molecular excited state, and the other non-radiative, where a jump is made from the S1 excited-state electronic manifold to the S0 manifold. A 3rd less probable possibility, intersystem crossing, is discussed below.  

Radiative Decay: Fluorescence

The 6 downward-pointing arrows connecting the S1 excited-state electronic state represent the spectrum of colours of light that might be emitted from a molecular excited state. The purple, blue, green, yellow, orange, and red arrows symbolize radiative decay pathways connecting S1, v=0 to the states S0, v=0 through S0, v=5 ground electronic states, correspondingly. The fluorescence will be emitted through peaks at different colours in the UV-visible spectrum because all of the transitions can be permitted, depending on their Franck-Condon overlap integrals, or Franck-Condon factors. Fluorescence is an extremely powerful spectroscopic method, since we have detectors capable of recording single photons. Therefore we can utilize fluorescence to identify where a molecule is (for example, in a microscope image), how many are present (we can notice a single molecule), and what the relative orientation of the molecule is.

Fluorescence is very sensitive to changes in the chemical environment. For molecules that have substantial transforms between their ground and first excited electronic states, the excited state energy evolves through the reorganization of the dipole moments of a polar solvent. This procedure is said solvatochromism, and is of huge value for characterizing the dynamical transforms in atmosphere that an excited state molecule experiences. Understanding such phenomena are still an active research difficulty, and are vital for understanding all of the characteristics that influence the outcomes of photo physical and photochemical procedures occurring from excited electronic states. 

Non-Radiative Decay: Internal Conversion

Internal conversion is the non-radiative decay method via that higher-lying electronic state can quickly relax to lower-lying states that have the similar spin multiplicity. This can hold true for singlet-singlet, triplet-triplet, and other states also. The case revealed in the diagram above symbolizes internal conversion from S1,v=0 to S0,v=0. Usually, internal conversion can take place between any vibrational levels in the initial and final electronic state.

Theoretical work done in the year 1970s via Prof. Karl Freed and co-workers illustrated that the probability for internal conversion enhances by the energy gap between the initial and final states. Internal conversion from higher-lying singlet states is extremely significant to life processes. Several instances comprise the non-radiative decay of the nucleic acid bases, and in chlorophyll and related light-harvesting pigments.

Internal Conversion: Importance to Life Processes

The computed excited state lifetimes of the 5 nucleic acid bases would be supposed to be about 10 nanoseconds depend on their structural similarity to a huge number of other organic molecules. Nevertheless, when illuminated via ultraviolet light in the 250-285 nm wavelength range, the 5 nucleic acid bases cytosine, adenine, thymidine, guanine, and uracil decay via a factor of about 20,000 times more speedily than we might or else expect: the lifetimes of the nucleic acid bases range from 0.29 to 0.72 picoseconds. It is accurately since of this unique property of the nucleic acid electronic structure that life shapes on this planet by genetic substance depends on DNA/RNA are capable to survive when our primary energy source is derived from sunlight: the quick internal conversion avoids other damaging excited-state photochemical procedures from occurring in DNA/RNA. When illumination via ultraviolet light is as well intense, then even this rapid molecular mechanism for dumping the UV light energy fails: photochemistry happens, particularly oxidative damage to guanines; carcinogenic lesions form, mutation rates skyrocket, and the organism dies from a number of reasons. An additional main instance of the significance of internal alteration to life processes is the truth that tetrapyrrole molecules (including porphyrins, hemes, and chlorophyll  a, exposed below) have extremely speedy relaxation from their higher-lying excited singlet states to a stable lowest excited state from that all photochemical reactions and photo physical procedures (these as intermolecular energy transfer) can occur. A common feature of the excited-state configurations of tetrapyrroles is that they have an extremely intense evolution at the edge of the UV-visible range (near 390-445 nm), by a molar extinction coefficient of about 106 M-1cm-1. This state is termed to not via its spectroscopic or electronic state label of S2 or S3, but rather as the Soret transition. The S2 and S1 states of chlorophyll a are called the Qx and Qy evolutions, correspondingly. Since such 3 transitions absorb strongly in the near UV to blue and red spectral ranges, chlorophyll a appears bright green in colour, since green is the only color of the visible spectrum not absorbed, therefore giving grass and tree leaves their green hue. Because the Soret excited state relaxes in about 1 picosecond via internal conversion, then proteins are engineered to build utilize of energy absorbed from sunlight via all three excited states, through the subsequent photochemical and photo physical procedures needing to be optimized only for the lowest energy excited state, S1.

Non-Radiative Decay: Intersystem Crossing                                            

Intersystem crossing attaches Spin-Paired (singlet) states to the Unpaired-Spin (triplet) States.  Although intersystem crossing in common isn't an elevated probability event, it is a method that links properly spin-forbidden transitions between states of different multiplicity. For instance, a spin- paired organic molecule in an excited singlet state can transform to a spin-unpaired state by a flip of the lone electron continuing in the Highest Occupied Molecular Orbital (HOMO). The probability for such a spin-flip evolution is negligible, except in the case where a vibronic energy level of the singlet is nearly degenerate through the energy of a triplet vibronic state. In the diagram above, The S1, v=2 state has been drawn to be only marginally higher in energy than the T1, v=4 state. When these a condition happens then the probability for the spin-flip intersystem crossing process is really enhanced. When a triplet state these as the green potential curve labelled T1 shown above is populated by intersystem crossing, the vibrational relaxation procedure will normally happen fairly quickly, lowering the energy of the triplet T1 state to the bottom of its vibronic potential energy well T1,v=0. As exposed above, the T1, v=0 state lies substantially below the S1, v=0 state, making a reverse intersystem crossing procedure have a very much lower probability than in the forward direction. Therefore, the only decay channel for T1, v=0 is to await the very low probability event that the T1, v=0 state can return to the S0 vibronic manifold. As conversed instantly above, the T1, v=0 excited-state decay can be either radiative or non-radiative. Unless there is an accidental near degeneracy (that happens less frequently than in the excited state case, as one can see via imagining carefully about the density of states in an enharmonic Morse potential for S1, T1, and S0) the T1 state can be fairly long-lived. At room temperature, triplet states might last for milliseconds, while at decreased temperatures, the triplet state can persist for minutes to hours.

Phosphorescence: Radiative Decay from Triplet States

In the event that a triplet state T1 is populated from an excited singlet state (these as S1), the evolution back to the ground electronic state S0 has an extremely low probability of occurring, and therefore happens infrequently. Nevertheless, such transitions do take place both non-radiatively (as in T1 to S1 intersystem crossing) and radiatively. When the transitions are accompanied via emission of light, this light has different spectral, but more highly, different time profiles for occurring. Since of the low evolution probability, the time scale for emission from triplet to singlet states via phosphorescence is on the millisecond to hour time frame, as is the case for non-radiative decay. By observing the time profile of the emission as well as the wavelength spectrum, the singlet-singlet fluorescence emission will take place on the nanosecond time scale, and the phosphorescence will happen much more gradually, on the millisecond and longer time scale. In the event that the intersystem crossing from the excited singlet state S1 to the triplet state T1 is very efficient, then nearly all of the excited singlet states can be changed to triplets. In this event, (which usually can only happen for several special cases of planar, symmetric molecules at low temperatures) the total phosphorescence production can be fairly intense, and easily observable by the human eye. Though, the probability for the phosphorescence transition is extremely low at any specified instant.

Photosensitization

Photosensitization is the process of initiating a reaction through utilize of a material capable of absorbing light and transferring the energy to the needed reactants. The method is usually utilized in photochemical work, mainly for reactions requiring light sources of indeed wavelengths that aren't willingly available. A commonly utilized sensitizer is mercury, which absorbs radiation at the year 1849 and 2537 angstroms; such are the wavelengths of light created in high-intensity mercury lamps. As well utilized as sensitizers are cadmium; numerous of the noble gases, particularly xenon; zinc; benzophenone; and a enormous number of organic dyes.

In a typical photosensitized reaction, as in the photodecomposition of ethylene to acetylene and hydrogen, a mixture of mercury vapour and ethylene is irradiated through a mercury lamp. The mercury atoms absorb the light energy, there being an appropriate electronic transition in the atom that corresponds to the energy of the incident light. In colliding through ethylene molecules, the mercury atoms shift the energy and are in turn deactivated to their original energy state. The excited ethylene molecules afterward undergo decomposition. Another mode of photosensitization examined in many reactions engages straight participation of the sensitizer in the reaction itself. 

The Franck-Condon Principle and the Stokes' shift

The energy levels are specified, as they generally are in spectroscopy, via correctly spaced horizontal lines. The lowest line symbolizes the ground state, E0, of the atom or molecule in which it survives in the absence of external activation. The higher lines (E1 and E2) symbolize excited electronic states--the only kind of excited states possible in an atom. In a diatomic or polyatomic molecule, one or several series of (also quantized) vibrational and rotational states are superimposed on each electronic state. If the molecule is complex, the diverse vibrational and rotational states lie extremely close mutually the sharp absorption (and emission) lines of atoms, or structured bands of easy molecules, are replaced by broad, continuous bands. The absorption lines (or bands) are represented, in schemes of this type, by arrows directed upwards and the emission lines or bands via arrows directed downwards (see the figure shown above). The energy of the quanta of emission or absorption is proportional to the lengths of the arrows. An atom or molecule can suck up only energy quanta equivalent to the distances between the permitted energy states. Once it is excited, say to state E2, it can liberate energy symbolized via downward arrows, leading from E2 to a lower energy state E1.

The wavy arrow in the above figure (from E2 to E1 ) relates to another, radiation less way in which a transition can occur by energy loss to surrounding molecules, or by its 'internal conversion' into vibrational energy of the excited molecule. The fall from E2 to E1 in one big jump is fluorescence. In fluorescence, light absorption leading, say, from E0 to E1 is repealed via light release leading from E1 to E0. When a photon is absorbed, the molecule usually is not merely transferred into an excited electronic state, but as well gains several vibrational energy. According to the so-called Franck-Condon principle, the absorption of a photon is a practically instantaneous procedure, since it engages only the rearrangement of practically inertia-free electrons. James Frank recognized the obvious: the nuclei are extremely heavy as evaluated to the electrons. Thus, during light absorption that happens in femtoseconds, electrons can shift, not the nuclei. The much heavier atomic nuclei have no time to readjust themselves during the absorption act, but have to do it after it is above and this readjustment conveys them into vibrations. This is best illustrated by potential energy diagrams these as that exposed in Figure. It is an expanded energy level diagram, by the abscissa acquiring the meaning of distance between the nuclei, rxy. The two potential curves illustrate the potential energy of the molecule as a function of this distance for 2 electronic states, a ground state and an excited state. Excitation is symbolized, according to the Franck-Condon principle, through a vertical arrow (A). This arrow hits the upper curve, except for extremely special cases, not in its lowest point, analogous to a non-vibrating state, but somewhere higher. This means that the molecule finds itself, after the absorption act, in a non-equilibrium state and begins to vibrate like a spring. This vibration is explained, in the figure, via the molecule running down, up, down again, and so on, along the upper potential curve, as a pendulum. The periods of such vibrations are of the order of 10-13, or 10-12 seconds. Because the common lifetimes of excited electronic conditions are of the order of 10-9 s, there is sufficient time during the excitation period for many thousands of vibrations. During this time, much (if not all) of the extra vibrational energy is lost via energy swap (temperature equalization) through the medium. The molecule, while it continues very "hot" as far as its electronic state is concerned, therefore acquires the ambient 'vibrational temperature.' Fluorescence, when it comes, originates from near the bottom of the upper potential curve, and follows a perpendicular arrow down (F), until it strikes the lower potential curve. Once more, it doesn't strike it in its deepest point, so that several excitation energy becomes altered into vibrational energy. The cycle absorption-release therefore encloses 2 periods of energy dissipation. Since of this, the fluorescence arrow (F) is always shorter (that is, the fluorescence frequency is lower) than that of absorption (A). In other words, the wavelengths of the fluorescence band are longer than of the absorption band. This displacement of fluorescence bands towards the longer wavelengths compared to the absorption bands (Stokes' shift) was a long-established experimental fact before the Franck-Condon principle provided its interpretation. Apparently, the extent of the shift based on the dissimilarity between the 2 potential curves. 

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Figure: Frank-Condon Principle. Potential energy curves for the ground state and an excited state of a diatomic molecule. (r, interatomic distance; A, absorption; F, fluorescence; numbers indicate vibrational states.) 

Franck-Condon Principle

A historical suggestion was that of James Franck (1925, who had shared, with Hertz, the 1925 Nobel Prize in Physics for the experimental confirmation of the quantum theory). He disputed merely that since of the huge masses of the nuclei in a molecule, their relative momentum can't be straight influenced by an electronic transition, so that those transitions will be most likely that conform most closely to a Principle. The nuclei don't move during an electronic transition. Thus, on a diagram of energy (ordinate) versus distance between the nuclei of a diatomic molecule (abscissa), this transition is vertical promoting the electron from the lowest vibrational state of a molecule in the ground state to a higher vibrational state of the excited state (for instance S1 or S2) of the molecule. The molecule in the excited state then dissipates immediately (within 10 to 100 fs) several energy as heat and the electron reaches the lowest vibrational level of the excited state. When the molecule relaxes to the ground state giving off light (fluorescence), it generally occurs at longer wavelength than the absorbing wavelength (Rotverschiebung, the red shift, Franck, 1927). The Franck-Condon principle, then, describes the examined red shift (Stokes, 1852) of the fluorescence spectrum from the absorption spectrum. The history of how the principle became recognized as the Franck-Condon principle was beautifully presented via Condon (1947). The original thought is in a paper at a Faraday Society meeting in London by Franck (1925); the proofs of this paper were sent to his student Hertha Sponer, who was then at the University of California at Berkeley on an International Education Board Fellowship. She kindly shared the proofs via Condon; he was able to generalize Franck's ideas (Condon, 1926). Condon (1947) states: "This work was all done in a few days. Doctor Sponer illustrated me Franck's paper one afternoon, and a week afterward all the quantitative work for my 1926 paper was done." 

The stokes' Shift

If a molecule is in a separated environment, these as in a gas phase, then the fluorescence is emitted from the lowest vibrational level of the excited state to the ground state and its vibrationally excited levels. This production has a spectrum that is a mirror image of the absorption spectrum. Where emission is excited via a narrow spectral source these as a laser, several release is at the similar wavelength as the excitation, and is recognized as "resonance fluorescence". For molecules in solution, the excited state can generally decrease its energy through rearrangement of the solvent 'cage' around the molecule prior to emission. In this case, although the emission spectrum is often still rather similar to a mirror image of the excitation spectrum, the absorption peak and the emission peak don't coincide. The emission maximum is now at longer wavelength (lower energy) than the excitation, and is said to be red-moved. 

Numerous factors affect the magnitude of the Stokes' shift. If the atmosphere is stiff so that little rearrangement is probable then the Stokes shift is supposed to be small. The magnitude of the shift based on factors these as solvent polarity, viscosity and polarizability. It as well based on whether the excited state can undergo any exact interactions these as proton transfer or charge transfer to other molecules or (sometimes) within the same molecule. Sometimes, there could be non-conformity to the mirror image rule. Such deviation is indicative of a change in geometry of the absorbing species soon after excitation and prior to emission. This implies that the ground state and the excited states now have different geometrical arrangements of their nuclei. Apart from change in geometry, excited state reactions could as well consequence in a breakdown of the mirror image rule. For instance the absorption and emission spectra of anthracene (in the presence of diethylaniline) aren't mirror images, due to the arrangement of a charge-transfer compound between the excited state of anthracene and diethyaniline.

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Figure: The Stokes' shift (displacement of fluorescence band compared to the absorption band of a molecule). Approximate mirror symmetry of the two bands exists when the shapes of the potential curves in the ground state and the excited state are similar. 

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