Showing papers on "Excited state published in 1971"

Perturbation theory of the non-linear optical polarization of an isolated system

Abstract: The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.

Synchronized Excitation of Fluorescence Emission Spectra

Abstract: THE fluorescence emission of complex mixtures of fluorescent compounds sometimes cannot be satisfactorily resolved by the usual technique of excitation at various fixed wavelengths selected specifically for individual components. Considerable improvement in such spectra often can be made when excitation and emission wavelengths are varied together, so that the fluorescence contributed by each component is restricted to that excited at wavelengths synchronously trailing the plotted emission.

Excited State Symmetry Assignment Through Polarized Two‐Photon Absorption Studies of Fluids

Abstract: We consider the effect of molecular symmetry on the two‐photon absorption constants of a randomly oriented sample of molecules. It is shown that a complete polarization study of an allowed two‐photon transition of a fluid generally yields enough information to permit an unequivocal identification of the symmetry species of the excited state. Ambiguities occur in only a few cases. Thus, oriented molecule studies for symmetry assignment will be largely unnecessary in two‐photon molecular spectroscopy. Symmetry assignment rules are given for all of the 32 crystallographic point groups and for the two groups of linear molecules. It is shown that certain transitions, which are allowed for two photons of different energies, are forbidden for two photons of the same energy. The application of this formalism to Raman scattering problems is discussed.

Quantum Statistical Theory of Superradiance. II

Abstract: We discuss the solution of the "superradiance master equation" derived in a preceding paper. During the first few photon transient times the cooperative atomic decay goes through a non-adiabatic oscillatory regime. For later times the decay takes place monotonically in time with the electromagnetic field following it adiabatically. The emitted light pulse has different statistical properties for an incoherently and a coherently prepared "superradiant" atomic initial state. The former case is characterized by large quantum fluctuations and strong atom-atom and atom-field correlations. In the latter case quantum fluctuations are small and the system behaves essentially classically. By also solving for a class of coherently prepared intermediate initial states we show that large quantum fluctuations occur only if the initial total occupancy of the excited state differs from the total number of atoms at most by a number of order unity.

Radiative transition probabilities within the 4 f 3 ground configuration of Nd:YAG

Abstract: The absolute intensities of 20 absorption bands between 2.5 and 0.25 μ have been measured for Nd:YAG at room temperature. These bands are forced electric dipole transitions between the4 I_{9/2} ground manifold and 34 excited J manifolds of the Nd3+ion. The transition intensities have been accounted for in terms of three phenomenological parameters with an rms error of 10 percent. The intensity parameters are used to evaluate the line strengths for excited-state absorption from the metastable4 F_{3/2} J manifold. Significant line strengths are predicted at wavelengths near 1.06 and 1.35 μ, suggesting the possibility of radiative depumping of the4 F_{3/2} upper laser level via the stimulated emission field.

Herzberg–Teller Vibronic Coupling and the Duschinsky Effect

Abstract: The assumption that the difference in composition, in terms of symmetry coordinates, between the normal vibrational motions of the ground and first excited state (Duschinsky effect) can be neglected in the Herzberg–Teller theory of absorption and fluorescence vibronic intensities is critically examined. A theory of the Duschinsky effect is described which involves expansion of the potential energy of the fluorescent state in terms of the ground state normal coordinate displacements. Off‐diagonal quadratic contributions arise in the expansion whenever there is a coupling between the crude Born–Oppenheimer electronic wavefunctions of the fluorescent and other excited states through two or more ground state normal motions of the same symmetry. The importance of the Duschinsky effect depends on the magnitudes of the Herzberg–Teller vibronic matrix elements and the frequency differences between the fundamentals which effect vibronic perturbations. Inclusion of the Duschinsky effect in the Herzberg–Teller theor...

Organic Dye Laser Threshold

Abstract: This paper describes the results of an investigation of the interrelated physical parameters that determine laser threshold for three organic dyes: rhodamine B, rhodamine 6G, and fluorescein. Not only are these dyes (rhodamine 6G in particular) among the most widely used and important laser dyes, but insights into the threshold condition derived from our studies of these particular dyes should be generally applicable to future dye laser research. Our detailed characterization of threshold for these dyes and our novel insights result from the use of triplet state spectral data in a thorough and quantitative way for the first time, coupled with the physically realistic approximation that the triplet population is proportional to the singlet excited state population. For the case of self‐tuning of the laser emission wavelength, solutions to the threshold equations are presented that establish relations between all the parameters affecting lasing: critical inversion, emission wavelength, extrinsic losses, dye concentration, length of active medium, and triplet to excited singlet population ratio. For reasonably high extrinsic cavity losses, the critical inversion is a simple power law function of extrinsic loss, and the emission wavelength is self‐tuned in such a manner that the ratio of extrinsic losses to intrinsic singlet absorption losses is substantially constant. There exists a region of low, but still physically realizable, cavity losses, where laser action is determined exclusively by intrinsic characteristics of the dyes (triplet absorption, singlet emission, and absorption). Asymptotic limits on the maximum wavelength of emission and on the minimum critical inversion appear in this region, beyond which there is no point in reducing extrinsic cavity losses. The fraction of triplet state molecules also determines long wavelength cutoffs for an externally tuned laser. Methods are outlined for measuring the ratio of triplet state to excited singlet state populations for dyes with known triplet absorption spectra and for determining semiquantitatively the triplet effects in dyes where this information is not known. A final interesting conclusion is that molecular modifications of rhodamine 6G cannot be expected to improve its threshold characteristics as a laser dye by much more than a factor of 4.

Photoelectron Spectra of the Halogens

Abstract: Photoelectron spectra of valence shell electrons in F2, Cl2, Br2, and I2 yield information on the molecular and electronic structure of the lowest several states of the corresponding positive ions, some of which is not available from previous spectroscopic studies. Spin–orbit fine structure is resolved for the ground 2Πg states of F2+ and Cl2+; values obtained are ζ = 337 ± 40 and 645 ± 40 cm−1, respectively. The first excited states of the ions are identified as 2Πu and approximate values of ζ = 2000–2200 and 6400 cm−1 obtained for Br2+ (A 2Πu) and I2+(A 2Πu), respectively. A state in F2+ reported previously [D. C. Frost, C. A. McDowell, and D. A. Vroom, J. Chem. Phys. 46, 4255 (1967)] to lie at ∼ 17.4 eV is not observed here and is attributed to nitrogen impurity. Vibrational frequencies for F2+ and Cl2+(X 2Πg) are in agreement with spectroscopic work. The corresponding frequencies for Br2+ and I2+ are ωe = 360 ± 40 and ∼ 220 cm−1. A change in bond length to Br2+(2Πg) of Δre ∼ (−)0.095 A is estimated fr...

Electrochemistry of excited molecules: photo‐electrochemical reactions of chlorophylls*

Abstract: Semiconductors with a sufficiently large energy gap, in contact with an electrolyte, can be used as electrodes for the study of electrochemical reactions of excited molecules. The behavior of excited chlorophyll molecules at single crystal ZnO-electrodes has been investigated. These molecules inject electrons from excited levels into the conduction band of the electrode, thus giving rise to an anodic photocurrent. The influence of various agents on this electron transfer has been studied. In the presence of suitable electron donors (e.g., hydroquinone, phenylhydrazine) in the electrolyte chlorophyll molecules, absorbing quanta, mediate the pumping of electrons from levels of the reducing agents into the conduction band of the semiconductor-electron acceptor. The electron capture by the semiconductor electrode is irreversible, when an adequate electrochemical gradient is provided in the electrode surface. An experimental technique for the study of the kinetics of photoelectrochemical reactions of chlorophyll molecules is introduced and a theoretical approach for its calculation is given. Some properties of excited chlorophyll at semiconductor electrodes (unidirectional electron transfer, highly efficient charge separation, chlorophyll as electron pump and able to convert electronic excitation into electric energy) show similarity to the behavior of chlorophyll in photosynthetic reaction centers.

Single‐Configuration Wavefunctions and Potential Curves for Low‐Lying States of He2+, Ne2+, Ar2+, F2−, Cl2− and the Ground State of Cl2

Abstract: Wavefunctions, orbital energies, and potential curves for He2+, Ne2+, Ar2+, F2−, and Cl2− have been calculated in the molecular‐orbital, self‐consistent‐field approximation over a range Re ≲ R < ∞ for the ground state and those excited states which dissociate into an atom and an ion in their ground states. The ground state potential curve for Cl2 has been calculated for R ∼ Re. Dissociation energies and other parameters obtained from the calculated potential curves are compared with corresponding parameters obtained from elastic differential scattering measurements and resonant electron capture in noble gases, measurements of afterglow line profiles in dissociative recombination radiation in neon and argon, optical absorption spectra of VK centers, and endoergic charge transfer studies of halogen ions and molecules. A formal analysis and discussion of the sources of correlation error in the calculated potential curves and a discussion of the expansion errors are also given.

Combined Configuration-Interaction—Hylleraas-Type Wave-Function Study of the Ground State of the Beryllium Atom

Abstract: A method is proposed for the accurate determination of atomic wave functions and energies by the explicit introduction of interelectronic coordinates into a configuration-interaction wave function. This is accomplished by choosing the configurations in the wave function to be antisymmetrized projected products of one-electron functions with powers of interelectronic coordinates. A 107-configuration wave function for the ground state of the beryllium atom was constructed from a basis set consisting of $s$ and $p$ Slater-type orbitals and powers of interelectronic coordinates: ${r}_{\mathrm{ij}}^{v} (v.=0,1,2)$. The energy obtained from this wave function ($E=\ensuremath{-}14.66654$ a.u.) is an upper bound to the "exact" nonrelativistic energy of this state and it is believed to be within 0.0002a. u. of the "exact" value. The advantages that the present method offers for extending accurate Hylleraas-method calculations to atomic systems with $Ng3$ are discussed.

Excitation of N2 and N+2 systems by electrons—I . Absolute transition probabilities

Abstract: Quantitative optical measurements of the N21P,2P and N+21N and Meinel systems, excited by electrons, have allowed measurements of transition probabilities, excitation cross-sections, and afterglow effects. This work is reported in two parts. The experiment and observations are described in detail in this article. Absolute transition probabilities have been derived for the N21P and the N+2M systems. Tables of values for the N22P and N+21N systems, compiled from earlier measurements, are included to provide a complete set for the four systems.

Theoretical Interpretation of the Optical and Electron Scattering Spectra of H2O

Abstract: Energies and potential surface characteristics are assigned to the first eight excited states of the water molecule. This assignment is shown to be consistent with all data from optical spectra, electron scattering, rotational distributions of the OH fragment in photodissociation and associated data, and with semi‐empirical INDO calculations. Energies and potential surfaces are given for the lowest resonant states of H2O−. These are consistent within the explainable error of the INDO calculations, as well as with the data on dissociative attachment and associative detachment in which H2O− is an intemediate for species. Assignment‐confirming experiments are suggested.

Formation of Vibrationally Excited OH by the Reaction H + O(3).

Abstract: Vibrationally excited hydroxyl formation by atomic hydrogen reaction with ozone, using Fourier transform spectroscopy

Self‐Consistent Molecular Orbital Methods. X. Molecular Orbital Studies of Excited States with Minimal and Extended Basis Sets

Abstract: Molecular orbital theory is applied to the excited states of a group of small molecules. Vertical transition energies are calculated using minimal and extended basis sets both with and without configuration interaction between singly excited states. The separate effects of extending the basis set and including CI are examined, and an evaluation of the over‐all performance at each level is made by comparing calculated results with experimental values. Minimal basis calculations with limited CI are found to describe adequately n→π* transition energies. Although triplet π→π* energies are reasonably described at this level, an extended basis set is necessary to obtain even a moderate approximation to singlet π→π* energies.

Critical Binding of an Electron to a Rotationally Excited Dipolar System

Abstract: Calculations are made of the minimum dipole moments necessary to bind an electron to a nonstationary finite electric dipole in a number of rotationally excited states. The critical moment for a given dipolar system is found to depend on the dipole length, the moment of inertia, and the rotational quantum state of the finite dipole. The properties of the dipolar system are discussed as to their implications for electron scattering by polar molecules.

Excited State Chemistry of the Ferrocyanide Ion in Aqueous Solution. I. Formation of the Hydrated Electron

Abstract: Excitation of the Fe(CN)64− ion in aqueous solution into the 1T1u or 1T2g excited singlet state, below 313 nm, leads to hydrated electron formation in competition with internal conversion to the lowest excited singlet 1T1g state. The limiting quantum yield of hydrated electron formation is a linear function of quantum energy between 313 and 228 nm, reaching φe≃ 0.9 at 228 and 214 nm. Above 313 nm hydrated electron formation is not observed, but photoaquation is. Dependence of Φe on scavenger (N2O) concentration is observed. The involvement of CTTS character in the process, and the role of rapid solvent rearrangement in the dissociation of the excited state, are discussed.

Kinetic Modeling of the High-Power Carbon Monoxide Laser

Abstract: A model for the kinetics of the cooled direct‐discharge‐excited carbon monoxide laser is presented. The kinetic mechanism responsible for creating the observed population inversions cannot be explained by simple one‐step resonance transfer between an excited metastable and the CO molecule, in view of the many vibrational bands which lase in this system. The present paper analyzes a kinetic model of the CO laser which includes the following processes: (a) Vibration‐to‐vibration (V‐V) energy exchange among the anharmonic vibrational states occurring in CO–CO collisions. (b) Resonance electron impact excitation of the lower CO vibrational states. (c) Radiative decay of the CO vibrational states. (d) Collisional quenching of vibrational excitation in CO–He collisions. Using a Morse anharmonic oscillator model of the CO vibrational states, kinetic equations are formulated which govern the individual vibrational state populations, subject to the preceding processes. The resulting set of nonlinear algebraic equations is solved by an interative technique for the steady‐state vibrational populations. Small‐signal laser gain is also predicted as a function of the following discharge conditions: (1) electron temperature, (2) electron concentration, (3) heavy species translational temperature, (4) CO partial pressure, and (5) He partial pressure. Comparison is made with recent experimentally obtained small‐signal gain data for the CO laser, as well as with other experimental results for CO lasers. It is shown that experimental results are consistent with an inversion created by electron impact excitation of the lower CO vibrational levels, followed by rapid redistribution of energy among the higher CO vibrational states via off‐resonant vibration‐vibration energy exchange. The present kinetic model successfully interprets the variation of gain with vibrational state, the observed strong temperature dependence of the gain, and the influence of He diluent in the discharge. The possibilities for using this pumping mechanism to obtain cw lasing with other diatomic species and in various laser configurations are also discussed.

Combined SCF and CI Calculations for the Low‐Lying Rydberg and Valence Excited States of Ethylene

Abstract: A series of nonempirical SCF–MO and CI calculations is carried out for the excited states of ethylene. In the usual manner the SCF treatment itself is seen to underestimate vertical transition energies from the closed‐shell ground state to open‐shell excited states by about 1 eV; an exception is noted, however, in the case of the π → π* singlet–singlet species. A CI(PCMO) treatment, which employs the SCF MO's of a given parent configuration as basis for its own CI expansion, is quite successful in balancing the correlation error, obtaining excellent agreement with experimental transition energies to valence and Rydberg states alike; a possible exception is found in the case of the π → π* singlet–singlet excitation for which the calculated value of 8.32 eV overestimates the location of the V ← N absorption maximum by 0.7 eV. The variational π* MO of the SCF wavefunction for the upper‐state singlet is quite diffuse, but it is argued that this fact is not inconsistent with the known experimental data for the V ← N band system. Since the calculated state is found to correlate with a valence species for antiplanar ethylene, its diffuse character in the planar geometry does not imply that its potential surface should resemble that of a Rydberg state; in addition, its charge density contours emphasize that it should not be associated with a pure Rydberg species even in the planar conformation. The change in character with relative rotation of the methylene groups suggests that the electronic transition moment must be considered explicitly in the theoretical treatment of the intensity distribution in the V ← N bands, and also indicates that the probability of nonvertical transitions to partially rotated structures may well be greater than that of the vertical excitation.

Electronic relaxation as a cause of diffuseness in electronic spectra

Abstract: Diffuseness, as seen in the vapour absorption spectra of polyatomic molecules, is related with rapid electronic relaxation (radiationless transitions). The causes common to both are perturbations between electronic states. Line broadening is related to excited state lifetimes through the uncertainty principle. To this end, twelve causes of diffuseness are first listed, and their incidence examined. A distinction is drawn between intrinsic diffuseness, associated with excitation to or perturbation by a (quasi-)continuum and including the electronic relaxation mechanism here proposed, and trivial diffuseness due to overcrowding of individually sharp lines. Trivial diffuseness may be temperature dependent (structureless rotational envelopes; overcrowded sequence bands) or, in very large molecules, temperature independent. I t has been shown that rotational envelopes should contain sharp features in a number of transitions which prove, experimentally, to be diffuse. Because of sequence bands, however, there is for any polyatomic molecule a fairly well-defined critical temperature, calculable from ground state vibrational data, above which the entire electronic spectrum must become structureless. This critical temperature decreases with increasing molecular size and with increasing molecular flexibility, and in conjunction with vapour pressure considerations sets definable limits to the kinds of molecule for which structured spectra can be obtained in the gas phase. But this mechanism is insufficient to explain the frequent occurrence of structureless spectra in small rigid molecules. The literature on medium to high resolution spectra of polyatomic molecules is then reviewed, to establish the generalization that the only transitions with structure (if any) will normally be the first triplet (if observable) and the first singlet, and possibly (for special reasons) Rydberg transitions. This survey is complemented by measurements on the following molecules: pyridine N-oxide, indene, indazole, purine, quinoline, isoquinoline, 1,6-naphthyridine, quinazoline, quinoxaline, 1,4,5- triazanaphthalene, biphenylene, fluorene, acridine, tetramethylcyclobutane-1,3- dione, and all monoalkylbenzenes from ethyl to t-butyl. The proposed generalization is found to have wide validity, though there are one or two undeniable exceptions and a few marginal cases. It is associated with Kasha's rule concerning states capable of emitting radiation, though the correlation between the two is not necessarily one-to- one. Taken together, these rules and the evidence on which they are based leave the electronic relaxation mechanism as the only satisfactory explanation so far offered for the widespread occurrence of diffuse electronic transitions in polyatomics. This matter can also be studied in pure and mixed crystals, if it is assumed, as now seems very probable, that the crystalline matrix induces no line-narrowing. Recent systematic work on line widths in crystal spectra a t 4°K by Hochstrasser and Marzzaccol is in full accord with the viewpoint advanced here.

Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules II. The Electronic States and Spectrum of Pyrazine

Abstract: Ab initio SCF and CI treatments of the ground state and n → π* and π → π* excited states of pyrazine, C4H4N2, are reported for the molecule in its ground state equilibrium geometry. In the case of n → π* transitions, the two symmetry combinations of nitrogen lone pair orbitals n1 and n2 are found to correspond to the description n+ ≈ n1 + n2 + λσ and n− ≈ n1 − n2 in which the n+ orbital has the higher orbital energy and is significantly more delocalized than n− by interaction with the pyrazine ring sigma system. This result leads to a significant splitting at the CI level of description of 1.4 eV between the B3u and B2g excited states which are derived from the orbital promotions n+ → π* and n− → π*, respectively. Calculated transition energies to the lowest n → π* excited states 3B3u and 1B3u of 3.56 and 4.22 eV, respectively, are in good agreement with experimental values. A low‐lying 3B1u(π → π*) state for which there exists indirect experimental evidence is found to occur between the 3B3u and 1B3u sta...

The lowest triplet state of Zn porphin

Abstract: Phosphorescence microwave double resonance experiments are reported on Zn porphin at 1·2 K In glassy solution very broad resonance transitions are observed However, for Zn porphin in a crystalline n-octane matrix—a system known for its sharp optical spectra (Shpolskii effect)—three pairs of microwave transitions with widths of a few MHz are found, all of them corresponding to a decrease in phosphorescence intensity By studying the behaviour of the signals for various methods of preparation of the sample and as a function of the optical bandwidth of excitation and detection, one pair of transitions could be assigned to monomeric solute molecules The corresponding zero-field splittings are |X - Z| = 1355, |Y - Z| = 806 MHz It was further established that by ‘pumping’ either of these transitions a third one can be detected at the difference frequency, so that the order of the levels must be X> Y>Z (or reverse) The results indicate that the molecule no longer possesses a four-fold axis in the excited st

Luminescence spectra and photocycloaddition of the excited coumarins to dna bases

Abstract: — The lowest excited singlet and triplet states of coumarin, psoralen, and 4-hydroxy-coumarin have been assigned to the (π,π*) type on the basis of the luminescence spectroscopy and MO calculations. The mechanism of photocycloaddition of courmarin and psoralen to thymine has been described in terms of the perturbational MO model and MO reactivity indices. All possible cycloaddition patterns have been examined. Results suggest that the 3,4-bond of coumarin in the excited state is somewhat more reactive than the same bond of psoralen in the excited state. It is also predicted that the 3,4-bond of psoralen in the triplet state is more reactive than the 4′, 5′-bond. The results have been favorably correlated with the electronic characteristics of excited coumarin molecules and with available experimental data on the relative yields of photoadducts.