We thank Dr. Andreas Tillack (Oak Ridge National Laboratory), Dr. Lewis Johnson (University of Washington), and Dr. Bruce Robinson (University of Washington) for developing the program for coarse-grained Monte Carlo simulations that was used to generate the structure of the molecular system presented in the Representative Results section. A.A.K. and P.F.G. are supported by a Collaborative research award from the College of Science, CSU East Bay. M.H. is supported by a Forever Pioneer fellowship from the Center for Student Research, CSU East Bay. C.M.I. and S.S. are supported by the U.S. Department of Defense (Proposal 67310-CH-REP) under the Air Force Office of Scientific Research Organic Materials Division.

The authors disclose no conflicts of interest.

The method presented here allows for multiple customizations. For instance, it is possible to modify the parameters of the DFT and TD-DFT calculations, including the density functional, basis set, and specific definition of the atomic point charges.
Using long-range corrected functionals, such as &#969;B97X, &#969;B97XD, or &#969;PBE, is recommended in order to obtain reasonable transition densities for transitions with charge-transfer character. It may be interesting to study to what extent t...

In the past two decades, solids and films that are made from aggregated organic molecules have found multiple applications in optoelectronic devices. Devices based on such materials have many attractive properties, including small weight, flexibility, low power consumption, and potential for cheap production using inkjet printing. Displays based on organic light emitting diodes (OLEDs) are replacing liquid crystalline displays as state of the art for mobile phones, laptops, television sets, and other electronic devices1,2,3,4. The importance of OLEDs for lighting applications is expected to increase in the coming years4. The performance of organic photovoltaic devices is steadily improving, with power conversion efficiencies above 16% recently reported for single-junction organic solar cells5. Organic materials also have the potential to disrupt other technologies, such as fiber-optic communications, where their use enables the development of electro-optic modulators with extremely high bandwidths of 15 THz and above6,7.
A major challenge in optimizing solid-state molecular materials for applications in optoelectronics is that typically their properties strongly depend on the nanoscale structure of the material. The production process allows defining the nanostructure of a material to some extent by using controlled growth techniques, such as chemical vapor deposition,8 templating of optically active molecules onto another material (i.e., a polymer matrix9,10), thermal annealing11,12, etc. However, nanoscale disorder is intrinsic to most molecular materials and usually cannot be eliminated entirely. Therefore, understanding how disorder affects the properties of a material and finding ways to engineer it for optimal performance is essential for the rational design of organic optoelectronic materials.
The degree of disorder in molecular materials is usually too great to treat it as a perturbation of a periodic crystalline structure with an electronic structure that can be described by band theory. On the other hand, the number of molecules that must be included in a simulation to reproduce the properties of a bulk material or a film is too great to use first principles quantum chemical methods like density functional theory (DFT)13,14 and time-dependent density functional theory (TD-DFT)15,16. Organic molecules with applications in optoelectronics typically have relatively large &#960;-conjugated systems; many also have donor and acceptor groups. Capturing the correct charge-transfer behavior in such molecules is essential to calculating their optoelectronic properties, but it can only be accomplished using long-range corrected hybrid functionals in TD-DFT17,18,19,20. Calculations that use such functionals scale super linearly with the size of the system and, at present, they are only practical for modeling the optoelectronic properties of individual organic molecules or small molecular aggregates that can be described using no more than ~104 atomic basis functions. A simulation method that could describe disordered materials that consist of large numbers of chromophores would be very useful for modeling these systems.
The magnitude of intermolecular interactions in molecular materials is often comparable to or smaller than the order of variation in the energetic parameters (such as the eigenstate energies or excitation energies) between individual molecules that make up the material. In such cases, multiscale modeling is the most promising approach to understanding and optimizing the optoelectronic properties of large disordered molecular systems21,22,23. This approach uses first-principles quantum chemical methods (usually DFT and TD-DFT) to accurately calculate the properties of individual molecules that compose the material. The Hamiltonian of a material sample that is large enough to represent the bulk molecular material (perhaps, by employing periodic boundary conditions) is then constructed using the parameters that were calculated for individual molecules. This Hamiltonian can then be used to calculate the optoelectronic parameters of a large molecular aggregate, a thin film, or a bulk molecular material.
Exciton models are a subclass of multiscale models in which excited states of a molecular material are represented in a basis of excitons: electron-hole pairs that are bound by Coulomb attraction24,25. For modeling many excited state processes, it is sufficient to only include Frenkel excitons26, where the electron and the hole are localized on the same molecule. Charge transfer excitons, where the electron and the hole are localized on different molecules, may need to be included in some cases (e.g., when modeling charge separation in donor-acceptor systems)27,28. Although exciton models are multiscale models that can be parametrized using only first-principle calculations on individual molecules, they still account for intermolecular interactions. The two primary interaction types that they can account for are (a) excitonic couplings between molecules that characterize the ability of excitons to delocalize across or transfer between molecules and (b) electrostatic polarization of the electron density on a molecule by the charge distribution on surrounding molecules. We have previously shown that both of these factors are important for modeling the optical and electro-optic properties of molecular aggregates, such as the optical absorption spectra29 and first hyperpolarizabilities30.
In this paper, we present a protocol for parametrizing exciton models that can be used to calculate the optical spectra and other optoelectronic properties of large molecular aggregates and bulk molecular materials. The excitonic Hamiltonian is assumed to be a tight-binding Hamiltonian24,25,
<img alt="Equation 1" src="/files/ftp_upload/60598/60598equ01.jpg" />
where &#949;i is the excitation energy of the ith molecule in the material, bij is the excitonic coupling between the ith and the jth molecules,&#160;&#226;i&#8224; and&#160;&#226;i are the creation and annihilation operators, respectively, for an excited state on the ith molecule in the material. The excitonic Hamiltonian parameters are found using TD-DFT calculations that are performed on individual molecules that make up the material. In these TD-DFT calculations, the charge distribution on all other molecules in the material is represented by electrostatic embedding of atomic point charges to account for electrostatic polarization of a molecule&#8217;s electronic density. The excitation energies, &#949;i, for individual molecules are taken directly from the TD-DFT calculation output. The excitonic couplings, bij, between molecules are calculated using the transition density cube method31, with the ground-to-excited state transition densities for the interacting molecules taken from the output of a TD-DFT calculation in Gaussian32 and post-processed using the Multiwfn multifunctional wavefunction analyzer33. For simulating the properties of bulk molecular solids, periodic boundary conditions may be applied to the Hamiltonian.
The current protocol requires that the user have access to the Gaussian32 and Multiwfn33 programs. The protocol has been tested using Gaussian 16, revision B1 and Multiwfn version 3.3.8, but should also work for other recent versions of these programs. In addition, the protocol uses a custom C++ utility and a number of custom python 2.7 and Bash scripts, the source code for which is provided under the GNU General Public License (Version 3) at https://github.com/kocherzhenko/ExcitonicHamiltonian. The calculations are intended to be performed on a machine running an operating system from the Unix/Linux family.

<table><tbody><tr><td>&lt;em&gt;Gaussian&lt;/em&gt; 16, revision B1</td><td></td><td></td><td></td></tr><tr><td>Multiwfn version 3.3.8</td><td></td><td></td><td></td></tr><tr><td>GNU compiler collection version 9.2</td><td></td><td></td><td></td></tr><tr><td>python 2.7.0</td><td></td><td></td><td></td></tr></tbody></table>

excitonic hamiltonians for calculating optical absorption spectra and optoelectronic properties of molecular aggregates and solids

Rational design of disordered molecular aggregates and solids for optoelectronic applications relies on our ability to predict the properties of such materials using theoretical and computational methods. However, large molecular systems where disorder is too significant to be considered in the perturbative limit cannot be described using either first principles quantum chemistry or band theory. Multiscale modeling is a promising approach to understanding and optimizing the optoelectronic properties of such systems. It uses first-principles quantum chemical methods to calculate the properties of individual molecules, then constructs model Hamiltonians of molecular aggregates or bulk materials based on these calculations. In this paper, we present a protocol for constructing a tight-binding Hamiltonian that represents the excited states of a molecular material in the basis of Frenckel excitons: electron-hole pairs that are localized on individual molecules that make up the material. The Hamiltonian parametrization proposed here accounts for excitonic couplings between molecules, as well as for electrostatic polarization of the electron density on a molecule by the charge distribution on surrounding molecules. Such model Hamiltonians can be used to calculate optical absorption spectra and other optoelectronic properties of molecular aggregates and solids.

In this section we present representative results for computing the optical absorption spectrum of an aggregate of six YLD 124 molecules, shown in Figure 3a, where the structure of the aggregate was obtained from a coarse-grained Monte Carlo simulation. YLD 124 is a prototypical charge-transfer chromophore that consists of an electron-donating group of diethyl amine with tert-butyldimethylsilyl protecting groups that is connected via a &#960; -conjugated bridge to the electron accep...

Watch this Scientific Journal Video about Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids at JoVE.com

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Here, we present a protocol for parametrizing a tight-binding excitonic Hamiltonian for calculating optical absorption spectra and optoelectronic properties of molecular materials from first-principles quantum chemical calculations.

Rational design of disordered molecular aggregates and solids for optoelectronic applications relies on our ability to predict the properties of such ...

excitonic-hamiltonians-for-calculating-optical-absorption-spectra

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Chemistry

Chemical Bonding: Molecular Geometry and Bonding Theories

SCIENTISTS IN ACTION

8.3K Views.  California State University, East Bay. Dit protocol vergemakkelijkt de bouw van excitonische Hamiltonians voor de efficiënte berekening van zowel optische absorptiespectra als de meer complexe opto-elektronische eigenschappen van bulkmoleculaire materialen. Onze techniek breekt uiterst rekenintensieve kwantumchemische berekeningen op bulk moleculaire materialen in veel meer beheersbare berekeningen van enkele moleculen die worden uitgevoerd met behulp van gemeenschappelijke kwantumchemische software. Onze methode kan helpen compu...

Video: Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, spin-flip scattering) is described, using experiments on GaMnAs as a prototype III-Mn-V system.&#160; Spectrally-resolved and time-resolved experimental configurations are described, including the use of zero-background autocorrelation techniques for pulse optimization.&#160; The etching process used to prepare GaMnAs samples for four-wave mixing experiments is also highlighted.&#160; The high temporal resolution of this technique, afforded by the use of short (20 fsec) optical pulses, permits the rapid spin-flip scattering process in this system to be studied directly in the time domain, providing new insight into the strong exchange coupling responsible for carrier-mediated ferromagnetism.&#160; We also show that spectral resolution of the four-wave mixing signal allows one to extract clear signatures of (s,p)-d hybridization in this system, unlike linear spectroscopy techniques.&#160;&#160; This increased sensitivity is due to the nonlinearity of the technique, which suppresses defect-related contributions to the optical response. This method may be used to measure the time scale for coherence decay (tied to the fastest scattering processes) in a wide variety of semiconductor systems of interest for next generation electronics and optoelectronics.

The technique of femtosecond four-wave mixing is described, including spectrally-resolved and time-resolved configurations. We illustrate the utility of this technique for the investigation of crucial physical properties in the III-V diluted magnetic semiconductors, afforded by its nonlinearity and high temporal resolution.

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, ...

Engineering

Spatial Separation of Molecular Conformers and Clusters

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules.

We present a technique that allows the spatial separation of different conformers or clusters present in a molecular beam. An electrostatic deflector is used to separate species by their mass-to-dipole moment ratio, leading to the production of gas-phase ensembles of a single conformer or cluster stoichiometry.

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold ...

Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems

This paper briefly describes how nanowires with diameters corresponding to 1 to 5 atoms can be produced by melting a range of inorganic solids in the presence of carbon nanotubes. These nanowires are extreme in the sense that they are the limit of miniaturization of nanowires and their behavior is not always a simple extrapolation of the behavior of larger nanowires as their diameter decreases. The paper then describes the methods required to obtain Raman spectra from extreme nanowires and the fact that due to the van Hove singularities that 1D systems exhibit in their optical density of states, that determining the correct choice of photon excitation energy is critical. It describes the techniques required to determine the photon energy dependence of the resonances observed in Raman spectroscopy of 1D systems and in particular how to obtain measurements of Raman cross-sections with better than 8% noise and measure the variation in the resonance as a function of sample temperature. The paper describes the importance of ensuring that the Raman scattering is linearly proportional to the intensity of the laser excitation intensity. It also describes how to use the polarization dependence of the Raman scattering to separate Raman scattering of the encapsulated 1D systems from those of other extraneous components in any sample.

The paper describes a method for producing extreme nanowires by melt infiltration into carbon nanotubes and how 1D systems may be characterized and investigated using Resonance Raman Spectroscopy to determine vibrational and optical excitation energies.

This paper briefly describes how nanowires with diameters corresponding to 1 to 5 atoms can be produced by melting a range of inorganic solids in the ...

High Resolution Phonon-assisted Quasi-resonance Fluorescence Spectroscopy

High resolution optical spectroscopy methods are demanding in terms of either technology, equipment, complexity, time or a combination of these. Here we demonstrate an optical spectroscopy method that is capable of resolving spectral features beyond that of the spin fine structure and homogeneous linewidth of single quantum dots (QDs) using a standard, easy-to-use spectrometer setup. This method incorporates both laser and photoluminescence spectroscopy, combining the advantage of laser line-width limited resolution with multi-channel photoluminescence detection. Such a scheme allows for considerable improvement of resolution over that of a common single-stage spectrometer. The method uses phonons to assist in the measurement of the photoluminescence of a single quantum dot after resonant excitation of its ground state transition. The phonon&#39;s energy difference allows one to separate and filter out the laser light exciting the quantum dot. An advantageous feature of this method is its straight forward integration into standard spectroscopy setups, which are accessible to most researchers.

The manuscript describes a method of phonon-assisted quasi-resonant fluorescence spectroscopy that incorporates both laser-limited resolution and photoluminescence (PL) spectroscopy. This method utilizes optical phonons to provide linewidth-limited resolution spectra of atom-like semiconductor structures in the energy domain. The method is also easily realized with a single spectrometer optical spectroscopy setup.

High resolution optical spectroscopy methods are demanding in terms of either technology, equipment, complexity, time or a combination of these. Here we ...

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Photonic band structure enables understanding how confined electromagnetic modes propagate within a photonic crystal. In photonic crystals that incorporate magnetic elements, such confined and resonant optical modes are accompanied by enhanced and modified magneto-optical activity. We describe a measurement procedure to extract the magneto-optical band structure by Fourier space microscopy.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by ...

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

The accurate molecular simulation prediction of vibrational spectra, and other structural, energetic and spectral characteristics, of photo-active metal-oxide surfaces in contact with light-absorbing dyes is an ongoing thorny and elusive challenge in physical chemistry. With this in mind, a molecular-dynamics (MD) simulation were performed by using optimized empirical potentials for a well-representative and prototypical dye-sensitized solar cell (DSC) solvated by a widely-studied room temperature ionic liquid (RTIL), in the guise of a [bmim]+[NTf2]- RTIL solvating an N719-sensitizing dye adsorbed onto 101 anatase-titania. In doing so, important insights were gleaned into how using a RTIL as the electrolytic hole acceptor modulates the dynamical and vibrational properties of a N719 dye, estimating the spectra for the DSC photo-active interface via Fourier transformation of mass-weighted velocity autocorrelation functions from MD. The acquired vibrational spectra were compared with the experiment spectra and those sampled from ab initio molecular dynamics (AIMD); in particular, various empirical-potential spectra generated from MD provide insight into how partial-charge charge parameterization of the ionic liquid affects vibrational spectra prediction. In any event, careful fitting of empirical force-field models has been shown to be an effective tool in handling DSC vibrational properties, when validated by AIMD and an experiment.

A dye-sensitized solar cell was solvated by RTILs; using optimized empirical potentials, a molecular dynamics simulation was applied to compute vibrational properties. The obtained vibrational spectra were compared with experiment and ab initio molecular dynamics; various empirical potential spectra show how partial-charge charge parameterization of the ionic liquid affects vibrational spectra prediction.

The accurate molecular simulation prediction of vibrational spectra, and other structural, energetic and spectral characteristics, of photo-active ...

Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals

In this work, we describe a protocol for a novel application of hyperspectral imaging (HSI) in the analysis of luminescent lanthanide (Ln3+)-based molecular single crystals. As representative example, we chose a single crystal of the heterodinuclear Ln-based complex [TbEu(bpm)(tfaa)6] (bpm=2,2&#8217;-bipyrimidine, tfaa&#8211; =1,1,1-trifluoroacetylacetonate) exhibiting bright visible emission under UV excitation. HSI is an emerging technique that combines 2-dimensional spatial imaging of a luminescent structure with spectral information from each pixel of the obtained image. Specifically, HSI on single crystals of the [Tb-Eu] complex provided local spectral information unveiling variation of the luminescence intensity at different points along the studied crystals. These changes were attributed to the optical anisotropy present in the crystal, which results from the different molecular packing of Ln3+ ions in each one of the directions of the crystal structure. The HSI herein described is an example of the suitability of such technique for spectro-spatial investigations of molecular materials. Yet, importantly, this protocol can be easily extended for other types of luminescent materials (such as micron-sized molecular crystals, inorganic microparticles, nanoparticles in biological tissues, or labelled cells, among others), opening many possibilities for deeper investigation of structure-property relationships. Ultimately, such investigations will provide knowledge to be leveraged into the engineering of advanced materials for a wide range of applications from bioimaging to technological applications, such as waveguides or optoelectronic devices.

Here, we present a protocol to obtain luminescent hyperspectral imaging data and to analyze optical anisotropy features of lanthanide-based single crystals using a Hyperspectral Imaging System.

In this work, we describe a protocol for a novel application of hyperspectral imaging (HSI) in the analysis of luminescent lanthanide (Ln3+)-based ...

Atomic Spectroscopy: Absorption, Emission, and Fluorescence

Atomic spectroscopy is a vital tool in elemental analysis, both qualitatively and quantitatively. It can be broadly divided into optical spectroscopy, mass spectroscopy, and X-ray spectroscopy methods. The optical spectroscopic methods are atomic absorption spectroscopy (AAS), atomic emission spectroscopy (AES), and atomic fluorescence spectroscopy (AFS). The first step in all three methods is atomization, where the solid, liquid, or solution-phase samples are converted into gas-phase atoms and ions.
In AAS, the gaseous samples interact with electromagnetic radiation and absorb photons with the exact energies that promote electrons of ground-state atoms to their excited states. For example, the unpaired 3s electron of the Na atom gets promoted to the 3p, 4p, or 5p orbital on the absorption of radiation of 285 nm, 330 nm, or 590 nm, respectively. The reduction in transmitted light of certain wavelengths is measured by the detector and visualized with an absorbance or transmittance spectrum.
In AES, the gas-phase atoms in the ground state are electronically excited with heat or electrical discharge energy. These short-lived, high-energy excited gas-phase atoms relax back to the ground state, emitting photons corresponding to the energy gap. The intensity of the emitted light is detected and converted to an electrical signal that gives a fingerprint of the sample. For instance, electronic transitions of excited Na atoms from the 3p, 4p, and 5p orbitals back to the 3s orbital result in emissions around 590 nm, 330 nm, and 285 nm, respectively. The emitted radiation is measured and processed into a spectrum.
In AFS, the ground-state gas-phase atoms are irradiated by a characteristic wavelength and promoted to the electronically excited state. Provided radiationless transition does not occur, the excited-state atoms relax to the ground state by fluorescing at the exact wavelength corresponding to the energy they absorbed. The detector is usually at a right angle to the source beam, where only fluorescence emissions should reach it.
Unlike molecular spectra, atomic spectra have sharp lines due to the absence of various rotational and vibrational energy states that lead to peak broadening in molecular spectra.

Atomic spectroscopy is a vital tool in elemental analysis, both qualitatively and quantitatively. It can be broadly divided into optical spectroscopy, ...

Analytical Chemistry

Unit 1

Atomic Spectroscopy

KEY TERMS AND CONCEPTS

Molecular Spectroscopy: Absorption and Emission

Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational and vibrational energy levels.&#160; Each energy level is separated by an energy gap, with the gaps between adjacent electronic, vibrational, and rotational levels varying significantly. The three types of energy levels in a diatomic molecule are shown in Figure 1.
<img alt="Figure1" src="/files/ftp_upload/13024/13024_PT_Figure_1.svg" style="text-align: center; height: 400px;" />
Figure 1: The three types of energy levels in a diatomic molecule.
A molecule can absorb energy in the form of a photon from electromagnetic radiation and use that energy to excite the molecule into a higher energy state. During this process, changes can occur in the rotation around a bond, the frequency of bond vibration, or the transition of an electron from its ground state (the lowest energy state) to an excited state (a higher energy level). When the excited-state molecule returns to its ground state, it emits radiation. The energy of the absorbed or emitted photon is equivalent to the energy gap between the two energy levels involved in the transition. Therefore, each transition is dependent on the wavelength or frequency of the radiation.
Due to the varying magnitudes of energy gaps, the wavelengths of radiation absorbed during these transitions differ. For example, the energy consumed or released during the transition of a specific rotation in a molecule is in the range of microwave radiation. In contrast, the energy of infrared radiation corresponds to changes in bond vibrations. Furthermore, photons in the UV&#8211;visible range can excite an electron to a different orbital, particularly in the case of molecules with conjugated double bonds.

Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational ...

Introduction to Molecular Spectroscopy

UV&ndash;Vis Spectroscopy: Molecular Electronic Transitions

In Ultraviolet&#8211;Visible (UV&#8211;Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this process, the electrons in a molecule transit from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), moving to a higher energy state. This transition and the types of orbitals involved are central to understanding how molecules interact with UV&#8211;Vis light. The energy differences between the HOMO and the LUMO are referred to as the bandgap, which typically ranges from 125 to 650 kJ/mol.
A group of atoms in a molecule responsible for absorbing radiation is called a chromophore. When a chromophore undergoes structural changes, both the energy and intensity of the molecule&#39;s absorption change. Molecules with different chemical structures have band gaps and absorb radiation at different wavelengths, producing different absorption spectra.
In molecular orbital theory, the energy levels of orbitals influence the types of electronic transitions that can occur. Typically, the lowest-energy occupied molecular orbitals are the &#963; orbitals, corresponding to &#963; bonds. Next in energy are the &#960; orbitals, followed by nonbonding (n) orbitals that contain an unshared pair of electrons. The highest energy levels are found in unoccupied or antibonding orbitals (&#960;* and &#963;*). Certain restrictions, known as selection rules, must be considered during electron transitions. One important selection rule states that transitions involving a change in an electron&#39;s spin quantum number are not allowed. Such transitions are called &#34;forbidden&#34;&#160;transitions. A common example is a transition from the n to &#960;* orbitals, which are often seen in molecules containing lone pairs.

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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