Introduction to Light Absorption

Transcription

1 Introduction to Light Absorption Light is electromagnetic radiation, i.e. it consists of an electric field that oscillates in both time and space, and a corresponding orthogonal magnetic field that oscillates with the same spatial and temporal periodicity. Color and light absorption relate to how this radiation interacts with matter. Although both the magnetic and the electric field can be absorbed by materials, the interaction of the electric field of light is about 10 5 stronger than that of the magnetic field. Thus, to a first approximation, we only concern ourselves with the interaction of the electric field of light with matter. Formally the term light is strictly applied to electromagnetic radiation perceivable by the human eye which limits its range from ~400 nm to ~700 nm as shown below. Violet Blue Green Blue-Green YellowOrange Red Wavelength (nm) However, in practice the term is used more loosely. CHEM. 535, SPRING

2 Light can be characterized by its frequency and its wavelength which are related by c = λν where c is the speed of light, λ is the wavelength of light and ν is the frequency of the oscillating electromagnetic radiation given in Hz. Planck showed that the energy of a photon of light can be related to its frequency by E = hν = hc/λ, where h is Planck s constant Thus, energy is a linear function of frequency and a reciprocal function of wavelength, which will be important a bit later. CHEM. 535, SPRING

3 Light Absorption When a molecule interacts with light and energy is absorbed, the molecule is said be excited. In such a case a transition occurs in which the molecule is excited from an initial state to a higher energy state. Within a one-electron approximation, this excitation is described as the promotion of an electron from a filled to an unfilled orbital (in the case of diamagnetic materials). Before After hν Several parameters can be used to characterize this transition, including the energy of the incident radiation required for the efficient absorption of the light and the inherent ability of the molecules to absorb radiation of the appropriate energy. By the Planck relation: E g,e = E excited state -E ground-state = hν, where ν is the energy of the photon corresponding to the energy gap between the states. CHEM. 535, SPRING

4 The energy is reported in several units, and the following may be helpful for translating between some common units you may come across in the literature. 1 ev = kcal/mol = 8065 cm -1 = 1240 nm. Color Our perception of color is determined by what wavelengths of radiation reach our eye and the sensitivity of receptors in our eye to various colors. The eyes have rods and cones, which convert light into the electrical impulses that the brain uses to perceive images. The rods function under low intensity conditions and provide images in shades of black, gray and white. This is referred to as scotopic vision. The cones process images of high intensity in color; this is referred to as photopic vision. Cones come in three varieties that correspond roughly to blue, green and red sensitivities. If all three cones are simultaneously excited then the image will appear white. If wavelengths of light from a certain region of the spectrum are absorbed by a material, then the materials will appear to be the complementary color. Thus, if blue light is absorbed the material will look yellow. CHEM. 535, SPRING

5 The graphic below crudely shows what color will be perceived when a material is absorbed in certain regions of the visible spectrum. Yellow Orange Red Violet Blue Absorbance Wavelength (nm) You will note that green is not indicated on the chart shown above. This is because materials that appear green actually absorb in the red and the blue (i.e. about 650 nm and 425 nm). CHEM. 535, SPRING

6 Band Shape and Color Our ability to perceive very small differences in color is rather extraordinary. I have personally noted that two samples that appear to have virtually identical absorption spectra, perhaps with minute differences in their tails, are clearly different colors. Very small changes in the shape of an absorption band (not only the position) will cause materials to appear different shades. In general, colors that we perceive as brilliant and bright have strong narrow absorption bands, whereas dull colors tend to have weaker and broader absorption bands as shown below. Extinction Coefficient ( l-m -1 cm -1 ) Brilliant Dull CHEM. 535, SPRING

7 Three properties are often used to characterize a color: 1. Hue distinguishes the color purity of the dominant color (i.e. red from yellow). The position of absorption maxima largely determines this property. 2. Saturation is the measure of the total light intensity from all three primary colors that is provided by the dominant primary color. For example, suppose you had a red color and you slowly increased the amount of blue and green light reaching the eye, then the mixture of the red, blue and green would contribute to the perception of white. White plus red would give pink. The hue would not have been altered, but the saturation would be lower. 3. Lightness of a color is changed by varying the intensity of all three primary colors by the same amount. For example, if the intensity of a red were increased it would appear brown. NOTE: You can experiment with these parameters using Microsoft Power Point. Draw a filled object, go to the fill icon, go to "more fill colors", then "custom". You can play with the hue, saturation, and luminosity and see what colors can be made. CHEM. 535, SPRING

8 Terms Applied to Changes in Spectra Changes in chemical structure or the environment lead to changes in the absorption spectrum of molecules and materials. There are several terms that are commonly used to describe these shifts, which you will see in the literature, and with which you should be familiar. Bathochromic: a shift of a band to lower energy or longer wavelength (often called a red shift). Hypsochromic: a shift of a band to higher energy or shorter wavelength (often called a blue shift). Hyperchromic: an increase in the molar absorptivity. Hypochromic: an decrease in the molar absorptivity. Hyperchromic Extinction Coefficient ( l-m -1 cm -1 ) Hypsochromic (Blue shifted) Hypochromic Bathochromic (Red shifted) Wavelength (nm) Solvatochromic: a change in the absorption characteristics observed upon changing the solvent environment in which the molecule is dissolved. A molecule that undergoes a bathochromic shift in a more polar solvent is said to be positively solvatochromic. A molecule that undergoes a hypsochromic shift in a more polar solvent is said to be negatively solvatochromic. CHEM. 535, SPRING

9 Photophysical Processes A Jablonski diagram shown below is commonly used to illustrate the various photophysical properties and processes of a molecule. S n T n k ic S 1 k isc k ic k abs k fl T 1 k ic k phos S 0 The states on the left side of the Jablonski diagram are labeled S 0, S 1 and S n. These labels refer to the fact that all of these states are singlet states, meaning that the total spin angular momentum for each state is zero. In such a case the electrons are said to be spin paired, and the molecule is diamagnetic. CHEM. 535, SPRING

10 Triplets S n T n k ic S 1 k isc k ic k abs k fl T 1 k ic k phos S 0 In contrast, the states on the right side of the Jablonski diagram are labeled T 1 and T n. For these states, the total spin angular momentum is 1, and such states are called triplet states. Molecules with triplet states are paramagnetic. Here, several processes are illustrated and are indicated by the rate constants that characterize the process shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence. CHEM. 535, SPRING

11 Photophysical Processes Light absorption is characterized by k abs and occurs on a time scale of ~10 15 sec -1. Because the mass of the electron is much less than that of the nuclei, a good approximation is that the nuclei remain fixed on the time-scale of light absorption and then relax to new equilibrium geometries subsequent to the absorption process. Internal conversion is a process by which excess energy is dissipated through heat by internal vibrations. It is characterized k ic and occurs on a time-scale of ~ >10 12 sec -1. This is the process by which the nuclei relax to their equilibrium position upon excitation and is a process by which molecules in an electronically excited-state can relax to the ground-state without the emission of a photon. Fluorescence is the process by which a molecule that has singlet spin multiplicity loses energy (typically back to its ground state) with emission of light. It is characterized by the k fl (or k ra ) which is typically on the time-scale of ~ sec -1. The fluorescence quantum yield, φ fl is given by: φ = # of photons emitted/ # of photons absorbed = k fl / Σ k for all processes leading to loss of excited-state population. CHEM. 535, SPRING

12 Intersystem Crossing Molecules can also change their spin multiplicity, thus going from a singlet state to a triplet state. This process called intersystem crossing is formally quantum mechanically forbidden and consequently the rate constant is usually rather small, K isc is typically sec -1. Chemical substitution and certain vibrations can increase this rate dramatically; this will be discussed later in this course. Phosphorescence is a process by which light is emitted upon relaxation from a state of different spin angular momentum to the ground state. Since processes involving change of spin angular momentum are quantum mechanically forbidden, the probability of phosphorescence is low and the rate constant for phosphorescence is typically very small, sec -1. CHEM. 535, SPRING

13 Spectroscopy The absorption characteristics of a molecule are typically obtained by illuminating a sample with a light source of intensity (I 0 ) and recording the transmitted intensity of the light while varying the wavelength of the source. In this manner one can measure the intensity of transmitted light (I) as a function of wavelength. A plot of (I/I 0 ) x 100 vs. wavelength gives the transmittance spectra. 100% Transmittance Wavelength (nm) The Beer-Lambert law relates the transmittance of a sample back to molecular parameters by the relation; log I 0 /I = εcl = A where A is the absorbance (a unitless quantity), l is the pathlength of the sample in cm, c is the concentration of the chromophore in the medium in mole-l -1 and CHEM. 535, SPRING

14 ε is the molar absorptivity or extinction coefficient with units of l-mole -1 cm -1. The extinction coefficient characterizes the ability of a molecule to absorb light at a given wavelength. Oscillator Strength and Molecular Parameters The total ability of a molecule to absorb light is given integrating the total area under the absorption peak, plotted in extinction coefficient vs. energy!!! (Note that a scale that is linear in wavelength is not linear in energy). f = ε ν f εmax ν12 / This integral is called the oscillator strength and is the probability that a molecule interacting with light over an energy range will be taken from one state to the other state under consideration. This can be related back to the wavefunction discussed by Professor Brédas by a term called the transition dipole moment. f = νµ 2 where ν is the mean absorption frequency of the band in cm 1. ge CHEM. 535, SPRING

15 Classically the interaction of an electric field ( E ) with a dipole µ is given by: Energy = r r E µ Dipole moment is related to the amount of charge separation over a given distance µ = e n q n r n Where e n is the elementary charge of particle n, (i.e. + or ), q n is the fractional charge on that particle and r n is the distance of that particle from a reference coordinate µ tot = e n q n r n n CHEM. 535, SPRING

16 Quantum Description of Dipole Moment Consider two electrons in p orbitals - the dipole moment of each particle is given by: e +r e r Quantum mechanically this is given by the following expression: µ = ψ*( e n r n )ψ τ n e n is charge on the n th particle r n is the position of the particle with respect to a coordinate system which is given more succinctly as: µ = ψ*(r)ψ τ CHEM. 535, SPRING

17 Consider Transition Between Two Different States A similar term the transition moment between two different states (for example g and e) is given by: µ 2 g,e ψ g *(R)ψ e τ 2 This integral relates the wavefunction of the molecule back to the oscillator strength and the extinction coefficient. CHEM. 535, SPRING

18 Odd and Even Functions and Transition Moments π hν π excited state transition dipole operator function ground state No overlap between ground- excited state wavefunctions Apply transition moment operator of the form y α r Result leads to nonzero integral i.e. nonzero transition dipole moment Functions are said to be even when f(x) = f( x) and odd when g(x) = g( x). The integral over all space of an even is non zero. The integral over all space for an odd function is exactly zero Using the rules for multiplication of functions i.e. even even = even; even odd = odd; odd odd = even CHEM. 535, SPRING

19 Thus, it is should be clear that, since R is odd, for molecules where the ground and excited state wavefunctions are even or odd, the ground- and excited-state wavefunctions must not have the same symmetry if the transition dipole moment is to be non-zero. excited state transition dipole operator function ground state No overlap between ground- excited state wavefunctions Apply transition moment operator of the form y α r Result leads to nonzero integral i.e. nonzero transition dipole moment Note the fact that if the two wavefunctions do not have the same symmetry this ONLY means that the transition moment will be non-zero; it provides no insight in the magnitude of the transition moment. The degree of spatial overlap between the ground- and excited wavefunctions plays a critical role in determining the magnitude of the transition dipole moment. CHEM. 535, SPRING

20 Pseudo-physical Description of Transition Dpole Moment Consider the evolution of the wavefunction for a particle in a box upon excitation from the ground state (with no nodes) to the first excited state with one node. Wavefunction Initial Instanteous with field Final Time Initially the function is symmetric with respect to the axis of the onedimensional box. In the final state it is also symmetrical, however you can envision a snapshot of the system as the light field is interacting with the wave-function wherein a node begins to develop as is shown in the middle and the wavefunction is evolving from the initial to final state. Now consider the electron density during this process that, is of course, the square of the wavefunction: Electron density Initial Symmetric Instanteous with field Transitory dipole present Final Symmetric Time As can be seen in the initial and final states the electron density is symmetrically distributed with respect to the axis of the box. However with the field on, the electron density is not symmetrically distributed and a transitory dipole moment can be present. CHEM. 535, SPRING

21 Back to Molecules This concept can be easily seen by considering the transition for ethylene. π π Now if the wavefunctions are considered to be linear combinations of atomic orbitals then: hν µ 2 g,e c i Φ i g i i * (R) ci Φ i e τ 2 This illustrates the need for there to be significant spatial overlap throughout the molecule between the ground- and excited-state wavefunction, if the transition moment that couples the two states is to be large. Furthermore, because of the position operator, R, if there is good overlap at sites that have a large distance from the origin of the coordinate system, these terms will have enhanced contributions to the transition dipole moment. Thus, molecules with good spatial overlap between two states that are not of the same parity (symmetry) will have large transition dipole moments and strong (allowed) transitions in the electronic spectrum Conversely, if any of the above criteria are not met, then the transitions will be weak. CHEM. 535, SPRING