3.3 Franck-Condon principle
2 min read•july 24, 2024
The explains how electronic transitions happen in molecules. It's all about the speed of these transitions and how they affect a molecule's structure. This principle helps us understand why absorption and look the way they do.
Advanced concepts build on this foundation, exploring vertical transitions and factors that influence vibronic transition intensity. These ideas are crucial for interpreting spectroscopic data and understanding molecular behavior during electronic excitation.
Fundamentals of the Franck-Condon Principle
Franck-Condon principle in electronic transitions
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- Franck-Condon principle states electronic transitions occur without changes in nuclear positions grounded in
- Electronic transitions happen much faster than nuclear motion typically ~ seconds
- Vertical transitions represented as vertical lines on potential energy diagrams
- measures overlap between vibrational wavefunctions determines transition probability
- Principle explains intensity patterns in absorption and emission spectra (UV-Vis spectroscopy)
Vibrational structure of spectra
- involve simultaneous changes in electronic and vibrational states
- Intensity distribution in spectra reflects overlap of vibrational wavefunctions governed by Franck-Condon factor
- show transitions from ground vibrational state to excited vibrational states intensity pattern relates to equilibrium geometry changes
- Emission spectra display transitions from lowest excited vibrational state to ground vibrational states often mirror image of absorption spectrum (exceptions exist)
- appears as series of peaks corresponding to transitions to different
- quantifies displacement between potential energy curves relates to number of visible vibronic transitions
Advanced Concepts and Applications
Vertical transitions and Franck-Condon principle
- Vertical transitions occur without changes in nuclear coordinates illustrated as straight vertical lines between on potential energy diagrams
- Concept exemplifies instantaneous nature of electronic transitions in Franck-Condon principle
- Results in population of higher vibrational levels in and non-equilibrium nuclear configuration immediately after transition
- Relaxation processes follow vertical transitions including vibrational relaxation to lowest vibrational level of excited state
- emerges as energy difference between absorption and emission maxima due to vertical transitions and subsequent relaxation
Factors in vibronic transition intensity
- Franck-Condon factor quantifies overlap of vibrational wavefunctions directly proportional to transition intensity
- Equilibrium geometry changes influence vibrational progression breadth and shape of potential energy curves
- Symmetry considerations determine allowed and forbidden transitions based on (benzene)
- Temperature effects impact initial state population distribution leading to in absorption spectra at higher temps
- Solvent interactions modify potential energy surfaces affect and transition intensities ()
- Vibronic coupling describes interaction between electronic and vibrational motions can cause intensity borrowing between electronic states
- Duschinsky effect involves mixing of normal modes between electronic states complicates interpretation of vibronic spectra
Key Terms to Review (24)
Absorption spectra: Absorption spectra refer to the specific wavelengths of light that are absorbed by a substance, revealing the unique electronic transitions that occur when molecules or atoms interact with light. Each element or compound has a distinct absorption spectrum, which acts like a fingerprint, allowing scientists to identify the presence of specific substances based on the light they absorb. Understanding absorption spectra is essential for grasping how energy transitions occur in atomic and molecular orbitals, how molecules respond during excitation states as described by the Franck-Condon principle, how spectral data can be interpreted to understand chemical environments, and how energy transfer happens in processes like photosynthesis.
Adiabatic vs. Non-adiabatic Transitions: Adiabatic transitions occur when a system changes its energy states without exchanging heat with its surroundings, while non-adiabatic transitions involve heat exchange during the process. In the context of molecular systems and photochemistry, these transitions are crucial for understanding how molecules move between electronic states, particularly in relation to the Franck-Condon principle, which describes the intensity of vibronic transitions based on the overlap of vibrational wave functions.
Born-Oppenheimer Approximation: The Born-Oppenheimer Approximation is a fundamental concept in molecular quantum mechanics that simplifies the treatment of molecular systems by separating electronic and nuclear motion. This approximation assumes that nuclei are much heavier and move much slower than electrons, allowing us to treat electronic states independently while considering nuclear dynamics later. This separation is crucial for understanding molecular vibrations, spectra, and the Franck-Condon principle, which relies on this approximation to explain the intensity of vibrational transitions in electronic transitions.
Electronic States: Electronic states refer to the distinct energy levels that electrons can occupy within an atom or a molecule. These states are crucial for understanding how electrons interact with light, leading to phenomena such as absorption and emission of photons. The arrangement of these states determines the allowed transitions between them, which is fundamental to concepts like spectroscopy and photochemistry.
Emission spectra: Emission spectra are the range of wavelengths emitted by atoms or molecules when they transition from a higher energy state to a lower energy state, releasing energy in the form of light. These spectra are unique to each element or compound, making them useful for identifying substances and understanding their electronic structures. The appearance of the emission spectrum is closely related to the Franck-Condon principle, which describes how molecular vibrations influence electronic transitions, and is essential for interpreting spectral data in various chemical contexts.
Excited State: An excited state refers to a higher energy state of an atom or molecule that occurs when it absorbs energy, causing one or more electrons to move to a higher energy level. This state is crucial for understanding processes like absorption and emission of light, as well as various electronic transitions within molecules.
Fluorescence spectroscopy: Fluorescence spectroscopy is a technique that measures the fluorescence emitted by a sample after it absorbs light, providing insights into the electronic and molecular structure of that sample. This method relies on the principle that when a molecule absorbs energy, it can transition to an excited state and then return to a lower energy state by emitting light. Key concepts such as molecular vibrations and electronic transitions play critical roles in understanding the mechanisms behind fluorescence, making this technique valuable for studying various chemical and biological systems.
Franck-Condon Factor: The Franck-Condon factor quantifies the probability of electronic transitions between different vibrational states during molecular transitions. It highlights how the overlap between vibrational wave functions of initial and final electronic states influences transition probabilities, linking closely to selection rules and the dynamics of non-radiative decay mechanisms.
Franck-Condon Principle: The Franck-Condon principle is a fundamental concept in photochemistry that describes the relationship between electronic transitions and molecular vibrations during the absorption and emission of light. It states that transitions between electronic states occur much faster than changes in nuclear configuration, meaning that the most probable transitions are those that involve minimal displacement of nuclear positions, leading to strong vibronic coupling.
Geometry optimization: Geometry optimization is a computational technique used in molecular modeling to find the most stable arrangement of atoms in a molecule. This process minimizes the potential energy of the system by adjusting atomic positions, which is crucial for understanding molecular structures, reactivity, and interaction with light. It plays an essential role in predicting molecular properties and behaviors, particularly in the context of electronic transitions and vibrational modes, which are fundamental aspects when applying concepts like the Franck-Condon principle.
Hot Bands: Hot bands refer to the spectral features observed in molecular spectroscopy that arise from transitions involving vibrational levels of a molecule that are populated in excited states, typically due to vibrational coupling or thermal excitation. These bands are important as they provide insight into molecular vibrational dynamics and the influence of temperature on the energy levels of molecules, connecting closely to the Franck-Condon principle which explains the intensity distribution of these transitions.
Huang-Rhys Factor: The Huang-Rhys factor is a dimensionless parameter that quantifies the strength of electron-phonon coupling in a material, particularly in the context of photochemistry and spectroscopy. It indicates how much the vibrational modes of a molecule influence the electronic transitions, playing a crucial role in determining the intensity of spectral lines and their shapes.
Molecular Symmetry: Molecular symmetry refers to the spatial arrangement of atoms in a molecule that remains unchanged under certain symmetry operations such as rotation, reflection, and inversion. This concept is vital for understanding how molecular structure influences various physical properties, including electronic transitions and vibrational modes, which are crucial when examining molecular behavior in processes like absorption and emission of light.
Photostability: Photostability refers to the ability of a substance, typically a chemical compound or material, to resist degradation or change when exposed to light. This property is crucial for understanding how substances behave under illumination, affecting their applications in various fields, such as photochemistry and photobiology. Photostability impacts the efficiency and longevity of light-sensitive materials, including pigments and pharmaceuticals, which can be influenced by factors like the Franck-Condon principle and singlet oxygen generation.
Potential Energy Surface: A potential energy surface (PES) is a multidimensional surface that represents the potential energy of a system as a function of its molecular geometries and configurations. It is crucial for understanding how molecular systems behave during chemical reactions, as it illustrates the energy changes associated with different spatial arrangements of atoms. The PES provides insights into reaction pathways, transition states, and the stability of molecular conformations, which are essential for grasping the Franck-Condon principle and its implications in spectroscopy and photochemistry.
Relaxed state: The relaxed state refers to the condition of a molecule when it is in its lowest energy configuration, typically after it has undergone excitation and then released energy, returning to a more stable form. This state is crucial for understanding molecular behavior during processes like fluorescence and phosphorescence, as it affects the probabilities of transitions between energy levels.
Solvatochromism: Solvatochromism is the phenomenon where the color of a substance changes due to alterations in the solvent environment. This property is particularly significant in photochemistry, as it can influence the electronic transitions of molecules, leading to shifts in their absorption and emission spectra based on solvent polarity and other characteristics. The way a solute interacts with different solvents provides insights into molecular behavior, which connects closely to selection rules and transition probabilities as well as the Franck-Condon principle.
Stokes Shift: Stokes Shift refers to the difference in wavelength (or energy) between the positions of the peak of the absorption spectrum and the peak of the emission spectrum of a substance. This phenomenon occurs due to the loss of energy in non-radiative processes and has significant implications in understanding molecular transitions, fluorescence, and phosphorescence.
Transition Dipole Moment: The transition dipole moment is a crucial concept in quantum mechanics that quantifies the probability of a transition between two electronic states in a molecule when exposed to electromagnetic radiation. This vector quantity plays a significant role in determining the selection rules for electronic transitions, influencing how and whether a molecule can absorb or emit light. It connects various phenomena such as electronic transitions, the Franck-Condon principle, and Stokes shifts, all of which are important for understanding molecular spectroscopy and photochemical processes.
Vertical Transition: A vertical transition refers to the change in electronic energy levels of a molecule without any change in nuclear geometry during a photochemical process. This concept is significant in understanding how molecules absorb light and subsequently move from a lower energy state to a higher energy state, while maintaining the same spatial arrangement of atoms, which is key to the Franck-Condon principle.
Vibrational Levels: Vibrational levels refer to the quantized energy states of a molecule associated with its vibrational motion. These levels are important in understanding how molecules absorb and emit light, especially when discussing transitions between electronic states and their coupling with vibrational states as seen in various spectroscopic techniques.
Vibrational Progression: Vibrational progression refers to the series of vibrational energy levels that molecules can access during electronic transitions, characterized by their distinct vibrational states. These progressions arise from the quantized nature of molecular vibrations and are significant in understanding how molecules absorb and emit light, especially under the Franck-Condon principle. This principle explains the intensity distribution of spectral lines as molecules transition between electronic states while vibrating in different modes.
Vibronic Coupling: Vibronic coupling refers to the interaction between electronic states and vibrational modes in a molecule, leading to mixing of electronic and vibrational wave functions. This coupling plays a crucial role in understanding how molecules transition between different energy states, particularly when considering selection rules, transition probabilities, and the behavior of excited states during processes like internal conversion and intersystem crossing.
Vibronic Transitions: Vibronic transitions refer to the simultaneous changes in both the electronic and vibrational states of a molecule during processes such as absorption or emission of light. These transitions are critical for understanding how molecules interact with light and are influenced by the molecular vibrations, leading to distinct spectral features. The concept is closely linked to the Franck-Condon principle, which describes the intensity distribution of vibronic bands based on nuclear positions in different electronic states.