DOCSLIB.ORG

Deuterium Isotope Effect in the Radiative Triplet Decay of Heavy Atom Substituted Aromatic Molecules

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Deuterium Isotope Effect in the Radiative Triplet Decay of Heavy Atom Substituted Aromatic Molecules Deuterium Isotope Effect in the Radiative Triplet Decay of Heavy Atom Substituted Aromatic Molecules J. Friedrich, J. Vogel, W. Windhager, and F. Dörr Institut für Physikalische und Theoretische Chemie der Technischen Universität München, D-8000 München 2, Germany (Z. Naturforsch. 31a, 61-70 [1976] ; received December 6, 1975) We studied the effect of deuteration on the radiative decay of the triplet sublevels of naph- thalene and some halogenated derivatives. We found that the influence of deuteration is much more pronounced in the heavy atom substituted than in the parent hydrocarbons. The strongest change upon deuteration is in the radiative decay of the out-of-plane polarized spin state Tx. These findings are consistently related to a second order Herzberg-Teller (HT) spin-orbit coupling. Though we found only a small influence of deuteration on the total radiative rate in naphthalene, a signi- ficantly larger effect is observed in the rate of the 00-transition of the phosphorescence. This result is discussed in terms of a change of the overlap integral of the vibrational groundstates of Tx and S0 upon deuteration. I. Introduction presence of a halogene tends to destroy the selective spin-orbit coupling of the individual triplet sub- Deuterium (d) substitution has proved to be a levels, which is originally present in the parent powerful tool in the investigation of the decay hydrocarbon. If the interpretation via higher order mechanisms of excited states The change in life- HT-coupling is correct, then a heavy atom must time on deuteration provides information on the have a great influence on the radiative d-isotope electronic relaxation processes in large molecules. effect. Besides this, deuteration must strongly affect Much work has been done concerning the nonradia- the 00-rate of the phosphorescence. Moreover, the tive decay. In 1972 Johnson and Ziegler2 found polarized phosphorescence excitation and emission that in the case of benzene, deuteration likewise spectra are expected to be sensitive to d-substitution. affects the radiative decay rate. This radiative d-iso- It is the aim of this paper to investigate the in- tope effect was interpreted in terms of vibronic fluence of d-substitution on the radiative rates of the interaction in the orbitally forbidden T1-S0-transition triplet sublevels of naphthalene in the presence of 3 4 of benzene. Later on, Lim and coworkers ' repre- heavy atoms in order to obtain further insight into sented a quantitative study of the luminescence of the various decay mechanisms of the lowest triplet aromatic hydrocarbons in an organic glass matrix. state in aromatic molecules. They found that the radiative d-isotope effect is a common feature in aromatic molecules, and that it may arise even in cases where the phosphorescence II. Experimental transition is not orbitally forbidden. Fischer and The experimental setup for measuring the degree Lim interpreted those observations in terms of a of polarization was described elsewhere 6. The band- non-adiabatic coupling 5. passes used were about 50 cm-1 in the emission In a recent study of the influence of a heavy atom region (in the case of naphthalene 100 cm"1) and on the various triplet decay mechanisms, Friedrich, about 100 cm-1 (naphthalene 200 cm-1) in the ab- Metz and Dörr proposed a connection between the sorption region. heavy atom effect and the d-isotope effect via a To determine the quantum yield, the spectral re- sponse of the detector side of the spectrometer was second order HT-coupling mechanism6'7. By ob- corrected by use of a tungsten band lamp (Osram). serving the polarization of the phosphorescence 00- The spectral emissivity of tungsten was taken from transition of haloaromatics, they found that the reference8. To produce corrected emission spectra automatically, a procedure was used originally em- ployed by Grüneis et al.9: The output of the lock-in Reprint requests to Dr. J. Friedrich, Institut für Physika- lische und Theoretische Chemie der Technischen Univer- amplifier (PAR mod 129) at a particular wave sität München, D-8000 München 2, Arcisstraße 21. number was multiplied by the corresponding cor- 62 J. Friedrich et al. • Deuterium Isotope Effect in a Radiative Triplet Decay reclion factor by use of PROM's (Programmable equations Read Only Memories). The fluorescence quantum kr = <I>vl (1 - T ; v> = <V/ (1 - * • yield, was obtained from the corrected emission The triplet lifetime r was measured by using a phase spectra using well established methods10. As a modulation technique. The exciting beam was reference standard we used diphenylanthracene in chopped at a suitable frequency and the phase shift EPA solution, the quantum yield of which is very of the emitted light was determined with the lock-in near to unity n'lla. amplifier. For those molecules which had a lifetime The phosphorescence quantum yield, &y>, was longer than the reciprocal cut-off frequency of the determined assuming that internal conversion from lock-in amplifier (5 cps) we used a shutter and a the first excited singlet state is negligible. Because of ary-recorder (HP 7045 A). the high energy gap, this approximation should All results were obtained in an elhanol matrix at hold very well in the case of the molecules con- 77 K. The dihalonaphthalenes investigated were syn- sidered. thesized from the corresponding diaminonaphtha- The quantum yield of the OO-transition, was lenes 12'12a. The substances were carefully purified determined by taking the ratio of the area of the by means of column chromatography and repeated 00-band and the area of the total phosphorescence sublimation. The Br- and I-derivatives were deu- spectrum. To be sure that the results were not in- terated by an exchange reaction with perdeutero- fluenced by reabsorption (we used concentrations benzene as a deuterium source13. In the case of of about 10~3m) we measured the quantum yield 1,4-dichloronaphthalene, deuteration was achieved of a very dilute solution (10-5m) of diphenyl- by starting the synthesis with perdeuteronaphthalene anthracene versus a 10~3m solution. The results (Merck). Thus, in this case, the isotopic purity agree within the error limit of the experiment. should exceed 98%. In the case of the I- and Br- The total radiative rate k and the 00-rate k° from derivatives, the degree of deuteration was deter- the lowest triplet stale were obtained from the mined from the NMR spectra to be at least 90%. Table 1. Quantum yields and rate constants of naphthalene and its derivatives. PG(O.)'La) and PG(0,i'Lb) represent the degree of polarization in the La and Lb-transition respectively, taken with respect to the 00-band of the phosphorescence. fcr°>'P and A"r0'0P denote the in-plane (ip) and the out-of-plane (op) polarized radiative rate constants of the lowest triplet to the vibrationless ground state of S0 . The errors in the various rates of naphthalene are somewhat larger due to the uncertainty in the determination of 0isC • 1,4-dichloronaphthalene 2,7-dibromonaphthalene 2,7-diiodonaphthalene naphthalene h6 d8 K d« h6 dB h8 d8 0F (±10%) 0.04 0.04 0.0009 0.0008 io-4 10~4 0.45 0.41 0ISO = 1-0F 0.96 0.96 1 1 1 1 0.55 0.59 (±0.1%) (±5%) (±4%) 0p (10%) 0.25 0.85 0.51 1 0.64 1 0.039 0.34 (±11%) (±11%) 0,,o 0.05 0.05 0.04 0.04 0.045 0.05 0.08 0.07 0p- <±10%> (±11%) (±11%) PG(O.VLa) -0.2 -0.2 -0.31 -0.315 -0.29 -0.29 -0.32 -0.32 (±2%) PG (0, J'Lb) -0.175 -0.205 -0.17 -0.2 -0.13 -0.16 -0.29 -0.29 (±2%) [sec"1] 9.1 1.8 200 59 1560 555 0.43 0.049 (±3%) 2 2 kr [sec-1] 2.4 1.6 102 59 1000 555 3.05X10- 2.9X10- (±10%) (±12%) (±12%) Ay [sec-1] 0.12 0.08 4.1 2.36 45 28 2.54X10"3 2.14X 10~3 (±10%) (±12%) (±12%) fcr°>°P [sec"1] 1.8 X 10 2 0.96 X 10 ~ 2 8.1X10 -1 3.4X10 1 10.6 5.75 1.3X10-4 l.ixio-4 (±11%) (±12%) (±12%) 3 A-ro.°P [sec"1] 0.1 0.07 3.3 2.0 34,4 23.3 2.4X10"3 2.03 X 10~ (±11%) (±12%) (±12%) 63 J. Friedrich et al. • Deuterium Isotope Effect in a Radiative Triplet Decay III. Results of polarization the influence of deuteration on the individual radiative rates from Tz and T!/ or T* In this section we summarize the principle find- (see Fig. 6). A few facts are obvious: ings from our results (see Tables 1 and 2). a) In naphthalene-d8 and -h8 there is no differ- ence in the degree of polarization when excited Table 2. Ratios of rate constants of the protonated and either in the Li,- or L;l-state. From this observation deuterated compounds. it follows that there is no different deuterium effect - e in the in-plane and in the out-of-plane polarized 2 = 3 V © <U 13 rates. II libromo ithalen 11 b) In the halonaphthalenes, especially in the case & & 1—1 — IM C <N C of the Br- and I-compounds, however, there is in- deed a significant change in the degree of polari- 5 3.4 2.8 8.8 zation upon deuteration with respect to Li,-excitation *(D) * ' (see Figure 5). MH) + 1.05 14%) 1.5 1.7 1.8 On the other hand, La-excitation produces no sig- (±17%) MD) nificant difference in the polarization of the phos- o kT° (H) i- 14%) 1.5 1.75 1.6 f l phorescence 00-transitions of the protonated and - kr° (D) T deuterated species respectively.
Load more

Recommended publications
  • Lecture 32 Relevant Sections in Text: §3.7, 3.9 Total Angular Momentum
    Physics 6210/Spring 2008/Lecture 32 Lecture 32 Relevant sections in text: x3.7, 3.9 Total Angular Momentum Eigenvectors How are the total angular momentum eigenvectors related to the original product eigenvectors (eigenvectors of Lz and Sz)? We will sketch the construction and give the results. Keep in mind that the general theory of angular momentum tells us that, for a 1 given l, there are only two values for j, namely, j = l ± 2. Begin with the eigenvectors of total angular momentum with the maximum value of angular momentum: 1 1 1 jj = l; j = ; j = l + ; m = l + i: 1 2 2 2 j 2 Given j1 and j2, there is only one linearly independent eigenvector which has the appro- priate eigenvalue for Jz, namely 1 1 jj = l; j = ; m = l; m = i; 1 2 2 1 2 2 so we have 1 1 1 1 1 jj = l; j = ; j = l + ; m = l + i = jj = l; j = ; m = l; m = i: 1 2 2 2 2 1 2 2 1 2 2 To get the eigenvectors with lower eigenvalues of Jz we can apply the ladder operator J− = L− + S− to this ket and normalize it. In this way we get expressions for all the kets 1 1 1 1 1 jj = l; j = 1=2; j = l + ; m i; m = −l − ; −l + ; : : : ; l − ; l + : 1 2 2 j j 2 2 2 2 The details can be found in the text. 1 1 Next, we consider j = l − 2 for which the maximum mj value is mj = l − 2.
    [Show full text]
  • Singlet/Triplet State Anti/Aromaticity of Cyclopentadienylcation: Sensitivity to Substituent Effect
    Article Singlet/Triplet State Anti/Aromaticity of CyclopentadienylCation: Sensitivity to Substituent Effect Milovan Stojanovi´c 1, Jovana Aleksi´c 1 and Marija Baranac-Stojanovi´c 2,* 1 Institute of Chemistry, Technology and Metallurgy, Center for Chemistry, University of Belgrade, Njegoševa 12, P.O. Box 173, 11000 Belgrade, Serbia; [email protected] (M.S.); [email protected] (J.A.) 2 Faculty of Chemistry, University of Belgrade, Studentski trg 12-16, P.O. Box 158, 11000 Belgrade, Serbia * Correspondence: [email protected]; Tel.: +381-11-3336741 Abstract: It is well known that singlet state aromaticity is quite insensitive to substituent effects, in the case of monosubstitution. In this work, we use density functional theory (DFT) calculations to examine the sensitivity of triplet state aromaticity to substituent effects. For this purpose, we chose the singlet state antiaromatic cyclopentadienyl cation, antiaromaticity of which reverses to triplet state aromaticity, conforming to Baird’s rule. The extent of (anti)aromaticity was evaluated by using structural (HOMA), magnetic (NICS), energetic (ISE), and electronic (EDDBp) criteria. We find that the extent of triplet state aromaticity of monosubstituted cyclopentadienyl cations is weaker than the singlet state aromaticity of benzene and is, thus, slightly more sensitive to substituent effects. As an addition to the existing literature data, we also discuss substituent effects on singlet state antiaromaticity of cyclopentadienyl cation. Citation: Stojanovi´c,M.; Aleksi´c,J.; Baranac-Stojanovi´c,M. Keywords: antiaromaticity; aromaticity; singlet state; triplet state; cyclopentadienyl cation; substituent Singlet/Triplet State effect Anti/Aromaticity of CyclopentadienylCation: Sensitivity to Substituent Effect.
    [Show full text]
  • Colour Structures in Supersymmetric QCD
    Colour structures in Supersymmetric QCD Jorrit van den Boogaard August 23, 2010 In this thesis we will explain a novel method for calculating the colour struc- tures of Quantum ChromoDynamical processes, or QCD prosesses for short, with the eventual goal to apply such knowledge to Supersymmetric theory. QCD is the theory of the strong interactions, among quarks and gluons. From a Supersymmetric viewpoint, something we will explain in the first chapter, it is interesting to know as much as possible about QCD theory, for it will also tell us something about this Supersymmetric theory. Colour structures in particular, which give the strength of the strong force, can tell us something about the interactions with the Supersymmetric sector. There are a multitude of different ways to calculate these colour structures. The one described here will make use of diagrammatic methods and is therefore somewhat more user friendly. We therefore hope it will see more use in future calculations regarding these processes. We do warn the reader for the level of knowledge required to fully grasp the subject. Although this thesis is written with students with a bachelor degree in mind, one cannot escape touching somewhat dificult matterial. We have tried to explain things as much as possible in a way which should be clear to the reader. Sometimes however we saw it neccesary to skip some of the finer details of the subject. If one wants to learn more about these hiatuses we suggest looking at the material in the bibliography. For convenience we will use some common conventions in this thesis.
    [Show full text]
  • Singlet NMR Methodology in Two-Spin-1/2 Systems
    Singlet NMR Methodology in Two-Spin-1/2 Systems Giuseppe Pileio School of Chemistry, University of Southampton, SO17 1BJ, UK The author dedicates this work to Prof. Malcolm H. Levitt on the occasion of his 60th birthaday Abstract This paper discusses methodology developed over the past 12 years in order to access and manipulate singlet order in systems comprising two coupled spin- 1/2 nuclei in liquid-state nuclear magnetic resonance. Pulse sequences that are valid for different regimes are discussed, and fully analytical proofs are given using different spin dynamics techniques that include product operator methods, the single transition operator formalism, and average Hamiltonian theory. Methods used to filter singlet order from byproducts of pulse sequences are also listed and discussed analytically. The theoretical maximum amplitudes of the transformations achieved by these techniques are reported, together with the results of numerical simulations performed using custom-built simulation code. Keywords: Singlet States, Singlet Order, Field-Cycling, Singlet-Locking, M2S, SLIC, Singlet Order filtration Contents 1 Introduction 2 2 Nuclear Singlet States and Singlet Order 4 2.1 The spin Hamiltonian and its eigenstates . 4 2.2 Population operators and spin order . 6 2.3 Maximum transformation amplitude . 7 2.4 Spin Hamiltonian in single transition operator formalism . 8 2.5 Relaxation properties of singlet order . 9 2.5.1 Coherent dynamics . 9 2.5.2 Incoherent dynamics . 9 2.5.3 Central relaxation property of singlet order . 10 2.6 Singlet order and magnetic equivalence . 11 3 Methods for manipulating singlet order in spin-1/2 pairs 13 3.1 Field Cycling .
    [Show full text]
  • The Statistical Interpretation of Entangled States B
    The Statistical Interpretation of Entangled States B. C. Sanctuary Department of Chemistry, McGill University 801 Sherbrooke Street W Montreal, PQ, H3A 2K6, Canada Abstract Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state. Whether or not the EPR spin pairs retain entanglement or disentangle, however, the statistical ensemble interpretation resolves the EPR paradox and gives a mechanism for quantum “teleportation” without the need for instantaneous action-at-a-distance. Keywords: Statistical ensemble, entanglement, disentanglement, quantum correlations, EPR paradox, Bell’s inequalities, quantum non-locality and locality, coincidence detection 1. Introduction The fundamental questions of quantum mechanics (QM) are rooted in the philosophical interpretation of the wave function1. At the time these were first debated, covering the fifty or so years following the formulation of QM, the arguments were based primarily on gedanken experiments2. Today the situation has changed with numerous experiments now possible that can guide us in our search for the true nature of the microscopic world, and how The Infamous Boundary3 to the macroscopic world is breached. The current view is based upon pivotal experiments, performed by Aspect4 showing that quantum mechanics is correct and Bell’s inequalities5 are violated. From this the non-local nature of QM became firmly entrenched in physics leading to other experiments, notably those demonstrating that non-locally is fundamental to quantum “teleportation”.
    [Show full text]
  • Quantum Mechanics
    Quantum Mechanics Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 5 1.1 Intendedaudience................................ 5 1.2 MajorSources .................................. 5 1.3 AimofCourse .................................. 6 1.4 OutlineofCourse ................................ 6 2 Probability Theory 7 2.1 Introduction ................................... 7 2.2 WhatisProbability?.............................. 7 2.3 CombiningProbabilities. ... 7 2.4 Mean,Variance,andStandardDeviation . ..... 9 2.5 ContinuousProbabilityDistributions. ........ 11 3 Wave-Particle Duality 13 3.1 Introduction ................................... 13 3.2 Wavefunctions.................................. 13 3.3 PlaneWaves ................................... 14 3.4 RepresentationofWavesviaComplexFunctions . ....... 15 3.5 ClassicalLightWaves ............................. 18 3.6 PhotoelectricEffect ............................. 19 3.7 QuantumTheoryofLight. .. .. .. .. .. .. .. .. .. .. .. .. .. 21 3.8 ClassicalInterferenceofLightWaves . ...... 21 3.9 QuantumInterferenceofLight . 22 3.10 ClassicalParticles . .. .. .. .. .. .. .. .. .. .. .. .. .. .. 25 3.11 QuantumParticles............................... 25 3.12 WavePackets .................................. 26 2 QUANTUM MECHANICS 3.13 EvolutionofWavePackets . 29 3.14 Heisenberg’sUncertaintyPrinciple . ........ 32 3.15 Schr¨odinger’sEquation . 35 3.16 CollapseoftheWaveFunction . 36 4 Fundamentals of Quantum Mechanics 39 4.1 Introduction ..................................
    [Show full text]
  • On Relational Quantum Mechanics Oscar Acosta University of Texas at El Paso, [email protected]
    University of Texas at El Paso DigitalCommons@UTEP Open Access Theses & Dissertations 2010-01-01 On Relational Quantum Mechanics Oscar Acosta University of Texas at El Paso, [email protected] Follow this and additional works at: https://digitalcommons.utep.edu/open_etd Part of the Philosophy of Science Commons, and the Quantum Physics Commons Recommended Citation Acosta, Oscar, "On Relational Quantum Mechanics" (2010). Open Access Theses & Dissertations. 2621. https://digitalcommons.utep.edu/open_etd/2621 This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. ON RELATIONAL QUANTUM MECHANICS OSCAR ACOSTA Department of Philosophy Approved: ____________________ Juan Ferret, Ph.D., Chair ____________________ Vladik Kreinovich, Ph.D. ___________________ John McClure, Ph.D. _________________________ Patricia D. Witherspoon Ph. D Dean of the Graduate School Copyright © by Oscar Acosta 2010 ON RELATIONAL QUANTUM MECHANICS by Oscar Acosta THESIS Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of MASTER OF ARTS Department of Philosophy THE UNIVERSITY OF TEXAS AT EL PASO MAY 2010 Acknowledgments I would like to express my deep felt gratitude to my advisor and mentor Dr. Ferret for his never-ending patience, his constant motivation and for not giving up on me. I would also like to thank him for introducing me to the subject of philosophy of science and hiring me as his teaching assistant.
    [Show full text]
  • Relativistic Quantum Mechanics 1
    Relativistic Quantum Mechanics 1 The aim of this chapter is to introduce a relativistic formalism which can be used to describe particles and their interactions. The emphasis 1.1 SpecialRelativity 1 is given to those elements of the formalism which can be carried on 1.2 One-particle states 7 to Relativistic Quantum Fields (RQF), which underpins the theoretical 1.3 The Klein–Gordon equation 9 framework of high energy particle physics. We begin with a brief summary of special relativity, concentrating on 1.4 The Diracequation 14 4-vectors and spinors. One-particle states and their Lorentz transforma- 1.5 Gaugesymmetry 30 tions follow, leading to the Klein–Gordon and the Dirac equations for Chaptersummary 36 probability amplitudes; i.e. Relativistic Quantum Mechanics (RQM). Readers who want to get to RQM quickly, without studying its foun- dation in special relativity can skip the first sections and start reading from the section 1.3. Intrinsic problems of RQM are discussed and a region of applicability of RQM is defined. Free particle wave functions are constructed and particle interactions are described using their probability currents. A gauge symmetry is introduced to derive a particle interaction with a classical gauge field. 1.1 Special Relativity Einstein’s special relativity is a necessary and fundamental part of any Albert Einstein 1879 - 1955 formalism of particle physics. We begin with its brief summary. For a full account, refer to specialized books, for example (1) or (2). The- ory oriented students with good mathematical background might want to consult books on groups and their representations, for example (3), followed by introductory books on RQM/RQF, for example (4).
    [Show full text]
  • Introduction to Unconventional Superconductivity Manfred Sigrist
    Introduction to Unconventional Superconductivity Manfred Sigrist Theoretische Physik, ETH-Hönggerberg, 8093 Zürich, Switzerland Abstract. This lecture gives a basic introduction into some aspects of the unconventionalsupercon- ductivity. First we analyze the conditions to realized unconventional superconductivity in strongly correlated electron systems. Then an introduction of the generalized BCS theory is given and sev- eral key properties of unconventional pairing states are discussed. The phenomenological treatment based on the Ginzburg-Landau formulations provides a view on unconventional superconductivity based on the conceptof symmetry breaking.Finally some aspects of two examples will be discussed: high-temperature superconductivity and spin-triplet superconductivity in Sr2RuO4. Keywords: Unconventional superconductivity, high-temperature superconductivity, Sr2RuO4 INTRODUCTION Superconductivity remains to be one of the most fascinating and intriguing phases of matter even nearly hundred years after its first observation. Owing to the breakthrough in 1957 by Bardeen, Cooper and Schrieffer we understand superconductivity as a conden- sate of electron pairs, so-called Cooper pairs, which form due to an attractive interaction among electrons. In the superconducting materials known until the mid-seventies this interaction is mediated by electron-phonon coupling which gises rise to Cooper pairs in the most symmetric form, i.e. vanishing relative orbital angular momentum and spin sin- glet configuration (nowadays called s-wave pairing). After the introduction of the BCS concept, also studies of alternative pairing forms started. Early on Anderson and Morel [1] as well as Balian and Werthamer [2] investigated superconducting phases which later would be identified as the A- and the B-phase of superfluid 3He [3]. In contrast to the s-wave superconductors the A- and B-phase are characterized by Cooper pairs with an- gular momentum 1 and spin-triplet configuration.
    [Show full text]
  • 15.1 Excited State Processes
    15.1 Excited State Processes • both optical and dark processes are described in order to develop a kinetic picture of the excited state • the singlet-triplet split and Stoke's shift determine the wavelengths of emission • the fluorescence quantum yield and lifetime depend upon the relative rates of optical and dark processes • excited states can be quenched by other molecules in the solution 15.1 : 1/8 Excited State Processes Involving Light • absorption occurs over one cycle of light, i.e. 10-14 to 10-15 s • fluorescence is spin allowed and occurs over a time scale of 10-9 to 10-7 s • in fluid solution, fluorescence comes from the lowest energy singlet state S2 •the shortest wavelength in the T2 fluorescence spectrum is the longest S1 wavelength in the absorption spectrum T1 • triplet states lie at lower energy than their corresponding singlet states • phosphorescence is spin forbidden and occurs over a time scale of 10-3 to 1 s • you can estimate where spectral features will be located by assuming that S0 absorption, fluorescence and phosphorescence occur one color apart - thus a yellow solution absorbs in the violet, fluoresces in the blue and phosphoresces in the green 15.1 : 2/8 Excited State Dark Processes • excess vibrational energy can be internal conversion transferred to the solvent with very few S2 -13 -11 vibrations (10 to 10 s) - this T2 process is called vibrational relaxation S1 • a molecule in v = 0 of S2 can convert T1 iso-energetically to a higher vibrational vibrational relaxation intersystem level of S1 - this is called
    [Show full text]
  • Measurement in the De Broglie-Bohm Interpretation: Double-Slit, Stern-Gerlach and EPR-B Michel Gondran, Alexandre Gondran
    Measurement in the de Broglie-Bohm interpretation: Double-slit, Stern-Gerlach and EPR-B Michel Gondran, Alexandre Gondran To cite this version: Michel Gondran, Alexandre Gondran. Measurement in the de Broglie-Bohm interpretation: Double- slit, Stern-Gerlach and EPR-B. Physics Research International, Hindawi, 2014, 2014. hal-00862895v3 HAL Id: hal-00862895 https://hal.archives-ouvertes.fr/hal-00862895v3 Submitted on 24 Jan 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Measurement in the de Broglie-Bohm interpretation: Double-slit, Stern-Gerlach and EPR-B Michel Gondran University Paris Dauphine, Lamsade, 75 016 Paris, France∗ Alexandre Gondran École Nationale de l’Aviation Civile, 31000 Toulouse, Francey We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics.
    [Show full text]
  • Empty Waves, Wavefunction Collapse and Protective Measurement in Quantum Theory
    The roads not taken: empty waves, wavefunction collapse and protective measurement in quantum theory Peter Holland Green Templeton College University of Oxford Oxford OX2 6HG England Email: [email protected] Two roads diverged in a wood, and I– I took the one less traveled by, And that has made all the difference. Robert Frost (1916) 1 The explanatory role of empty waves in quantum theory In this contribution we shall be concerned with two classes of interpretations of quantum mechanics: the epistemological (the historically dominant view) and the ontological. The first views the wavefunction as just a repository of (statistical) information on a physical system. The other treats the wavefunction primarily as an element of physical reality, whilst generally retaining the statistical interpretation as a secondary property. There is as yet only theoretical justification for the programme of modelling quantum matter in terms of an objective spacetime process; that some way of imagining how the quantum world works between measurements is surely better than none. Indeed, a benefit of such an approach can be that ‘measurements’ lose their talismanic aspect and become just typical processes described by the theory. In the quest to model quantum systems one notes that, whilst the formalism makes reference to ‘particle’ properties such as mass, the linearly evolving wavefunction ψ (x) does not generally exhibit any feature that could be put into correspondence with a localized particle structure. To turn quantum mechanics into a theory of matter and motion, with real atoms and molecules comprising particles structured by potentials and forces, it is necessary to bring in independent physical elements not represented in the basic formalism.
    [Show full text]