Density Matrix Treatment Research Articles

Microscopic Based Density Matrix Treatments of Electron-Transfer Reactions in Condensed Phases

Several non-phenomenological density matrix treatments of electron-transfer (ET) reactions in condensed phases are developed and examined. The methods consider the donor and acceptor system (the solute) under the influence of the surrounding fluctuating solvent. The main emphasis is placed on semiclassical methods, where the starting point is the Hamiltonian of the quantum mechanical electronic states of the solute. The diagonal elements of the Hamiltonian include the fluctuations of the solute electronic energies as a result of the interaction between the solute and the field from the classically moving solvent molecules. The fluctuating Hamiltonian is used to construct a Liouville equation, which is treated by three approaches. The first method is based on a direct numerical integration of the relevant Liouville equation. The second involves the use of a second-order Liouville equation, and the third involves the use of a Redfield type equation. The methods are examined by simulating electron transfer b...

Theory of the Relaxation Processes for Multilevel Spin Systems in Dilute Paramagnetic Solids at High Temperature

A direct density matrix treatment of the relaxation processes in dilute paramagnetic solids at high temperature is performed. Using the dressed state' formalism, the theory is developed differently from the one often referred to as the Redfield Theory, which uses the concepts of correlation function and relaxation matrix. General expressions for the linewidths and spin-lattice relaxation rates are obtained in the high temperature limit, for a lattice with infinite specific heat and up to strong microwave fields. In addition, the theory predicts experimental proofs for those cases where the concept of relaxation matrix ceases to be correct, or the lattice cannot be considered as having an infinite specific heat.

Nonadiabatic interaction effects on population transfer inH2by stimulated Raman transition with partially overlapping laser pulses

We have theoretically investigated the population transfer in a four-level ${\mathrm{H}}_{2}$ system by stimulated Raman transition from the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}({\ensuremath{\nu}}_{g}{=0,J}_{g}=0)$ level to higher rovibrational levels $({\ensuremath{\nu}}_{f}{,J}_{f})$ of the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state via the excited intermediate $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}({\ensuremath{\nu}}_{i}{=14,J}_{i}=1)$ and $C{}^{1}{\ensuremath{\Pi}}_{u}^{+}({\ensuremath{\nu}}_{i}{=3,J}_{i}=1)$ levels coupled with each other by nonadiabatic interaction, using time-dependent overlapping pump and Stokes laser fields. The density-matrix treatment, which permits the convenient inclusion of the spontaneous emissions from the intermediate levels, has been employed to describe the dynamics of the two-photon Raman resonance process. The present study performs the calculations of final populations (after both the pulses are over) of the ground and terminal levels for Q-branch ${(J}_{f}=0)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ and first overtone $({\ensuremath{\nu}}_{f}=2)$ transitions and the S-branch ${(J}_{f}=2)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ transition as a function of time delay between the two pulses for the cases of on-resonance as well as off-resonance excitations in a wide range $(2\ifmmode\times\else\texttimes\fi{}{10}^{5}--2\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ of peak intensities ${I}_{P}^{0}$ ${(I}_{S}^{0})$ of the pump (Stokes) fields. Both fields are assumed to have the same temporal shape, duration, peak intensities, and linear parallel polarizations. The accurate values of spontaneous radiative relaxation rates of the intermediate levels to the initial and final levels, taking into account their J and M dependence, are explicitly included in our calculations. The pulse width (full width at half maximum) ${\ensuremath{\tau}}_{p}$ is taken as 170 ns so that total spontaneous decay can occur during the pulse duration. The transfer efficiency is found to be very sensitive to the peak intensities of the laser pulses in each case of transition considered. Special attention is paid to the effects of the nonadiabatic (NA) interaction between $B(14,1)$ and $C(3,1)$ levels on population transfer efficiency. Calculations are also done in some particular cases using the adiabatic Born-Oppenheimer (ABO) approximation. The results with ABO approximation are found to differ remarkably from those obtained including NA interaction. Our calculations for the four-level ${\mathrm{H}}_{2}$ system reveal that almost complete population is transferred in counterintuitive pulse order for both on-resonance and off-resonance excitations with intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$ For intuitive pulse sequence also a large population transfer is achieved for on-resonance excitation at intermediate values of ${I}_{P}^{0}$ ${(I}_{S}^{0})$ and for off-resonance excitation at intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$

Resonant Luminescence in Semiconductor Quantum Dots under Two-Photon Excitation

We investigated the resonantly-excited fluorescence in a system of semiconductor quantum dots. By using a two-photon scattering technique, we observed the background-free resonant emission by eliminating the nonresonant contribution. The resonant signal consists of two spectral components corresponding to the contributions of scattering and luminescence. The linewidth of the luminescence component was found to depend on temperature, which reflected the exciton phase relaxation. These features are well explained in terms of the density-matrix treatment for a single atomic dipole.

The boundary between liquidlike and solidlike behavior in magnetic resonance

Recent experimental work in two-dimensional solution NMR (nuclear magnetic resonance) has demonstrated anomalous cross-peaks and additional resonances due to dipolar couplings between distant nuclei. These spectra have been analyzed either classically, using Bloch equations which include a mean-field approximation to the demagnetizing field, or quantum mechanically, using a full density matrix picture which shows that the peaks correspond to intermolecular multiple-quantum coherences (iMQCs). Here we use a density matrix treatment to predict intensities in solution for dipolar effects conventionally seen in solids; we also explore in detail the fundamental differences between dipolar effects in solids and liquids. For example, even though polarization transfer via the dipolar Hamiltonian in solution is not possible, indirect detection with substantial signal enhancement is possible. We find that, even for high-γ nuclei such as H1 or He3, solidlike dipolar effects are quite small unless the diffusion constant is roughly one million times smaller than that of water—which means that deviations between the quantum and classical treatments are barely observable in solution NMR, and that even solid He3 has liquidlike dipolar effects in agreement with experiment. However, the dipolar correlation function has an extremely unusual functional form—the long time falloff is proportional to t−3/2, not the exponential one commonly encounters. Because of this long falloff, solidlike dipolar effects can be substantial in solution electron spin resonance, and the classical picture of the demagnetizing field would fail in that case.

Fluorescence into Flat and Structured Radiation Continua: An Atomic Density Matrix without a Master Equation

We investigate an atomic $\Lambda$-system with one transition coupled to a laser field and a flat continuum of vacuum modes and the other transition coupled to field modes near the edge of a photonic band gap. The system requires simultaneous treatment of Markovian and non-Markovian dissipation processes, but the photonic band gap continuum can not be eliminated within a density matrix treatment. Instead we propose a formalism based on Monte-Carlo wavefunctions, and we present results relevant to an experimental characterization of a structured continuum.

Effect of A Magnetic Field on Photophysical Processes of Molecules

AbstractA main purpose of this paper is to present a density matrix treatment of the magnetic quenching of molecular luminescence. Unlike the previous theories, which only consider the magnetic effect on the nonradiative rate constant, the present theory describes the time‐evolution of the system under the action of a magnetic field. Our theory can treat both the steady state and transient molecular luminescence affected by a magnetic field.

The resonance fluorescence polarization of free rotors: Methyl iodide in methane and carbon dioxide

The polarization of the resonance fluorescence of symmetric top rigid rotors is described by a third-order density matrix treatment of resonance emission and a sum-over-all-rovibronic states scattering-tensor invariant framework. Within this theoretical approach the resonance fluorescence depolarization is a function of the excited electronic state population and rovibronic coherence decay rates, as well as the electronic absorption/emission line shapes. This description of the depolarization of resonance fluorescence is contrasted with that of resonance Raman in terms of angular momentum selection rules and dependence on material relaxation parameters. In contrast to resonance Raman emission in solution, the accompanying resonance fluorescence polarization is found to be most sensitive to the resonant excited state lifetime when this population decay time is of the order or less than rotational periods. These effects are demonstrated for excitation resonant with the B-state origin of CH3I vapor in high pressures of CH4 and CO2. The solute–solvent interaction responsible for the pure dephasing of the resonant optical coherence does not appear to cause orientational redistribution of the excited chromophore, at least on the time scale of the CH3I B-state origin lifetime. The influence of excited electronic B-state rovibrational pure-dephasing effects on the resonance fluorescence polarization measurements are discussed.

Spin-1 Double Quantum Spectroscopy in the Isotropic Phase: INADEQUATE Spectra of2H,2H and6Li,6Li AX Spin Systems

A density matrix treatment is presented which describes the main features of INADEQUATE experiments for spin-1 AX spin systems. It is shown that apart from two-spin double quantum peaks, which carry correlation information, one-spin double quantum peaks are to be expected. In the latter, homoculear spin–spin coupling is amplified in the F1 domain where the signal splitting amounts to 4J. The theoretical predictions are verified for the 2H,2H AX system of 3,3′-[D2]norcamphor. In addition, experimental results for a 6Li,6Li A2X2 or AA′XX′ spin system are presented and the influence of spin–lattice relaxation on the relative intensity of the one-spin double quantum peaks for 6Li,6Li experiments is demonstrated.

Spin-1 Double Quantum Spectroscopy in the Isotropic Phase: INADEQUATE Spectra of 2H,2H and 6Li,6Li AX Spin Systems

A density matrix treatment is presented which describes the main features of INADEQUATE experiments for spin-1 AX spin systems. It is shown that apart from two-spin double quantum peaks, which carry correlation information, one-spin double quantum peaks are to be expected. In the latter, homoculear spin–spin coupling is amplified in the F1 domain where the signal splitting amounts to 4J. The theoretical predictions are verified for the 2H,2H AX system of 3,3′-[D2]norcamphor. In addition, experimental results for a 6Li,6Li A2X2 or AA′XX′ spin system are presented and the influence of spin–lattice relaxation on the relative intensity of the one-spin double quantum peaks for 6Li,6Li experiments is demonstrated.

Quantum treatment of the effects of dipole–dipole interactions in liquid nuclear magnetic resonance

Experimental observation of anomalous intermolecular cross-peaks in two-dimensional solution NMR spectra have attracted significant recent attention. Extremely simple pulse sequences on extremely simple samples with large equilibrium magnetization give resonances in the indirectly detected dimension which are simply impossible in the conventional density matrix framework of NMR. Here we extend a recently proposed density matrix treatment [Science 262, 2005 (1993)] to calculate the exact time evolution for a variety of pulse sequences. This density matrix treatment explicitly removes two fundamental assumptions of the standard theory—it includes the dipolar interaction between spins in solution (which is only partially averaged away by diffusion) and completely removes the high temperature approximation to the equilibrium density matrix [exp(−βℋ)≊1−βℋ]. We compare this quantum mechanical treatment to a corrected classical model, which modifies the dipolar demagnetizing field formulation to account for the effects of residual magnetization, and show that the quantum picture can be reduced to this corrected classical model when certain assumptions about the retained dipolar couplings are valid. The combination of quantum and classical pictures provides enormously better predictive power and computational convenience than either technique alone.

Orientational quadrupolar glass in ortho-para hydrogen mixtures. I. Mean-field microscopic theory

The mean-field theory of the quadrupolar glass (QG) is presented using a microscopic approach. It is shown that the reaction-polarization effects caused by short-range spatial correlations are well distinguished from those of random-bond spin glasses. They control the QG concentration threshold and result in an incomplete orientational order. The QG ground state (zero quadrupolization, unsaturated Edwards-Anderson-type orientational order parameter) is predicted. Thermodynamic characteristics, namely entropy, pressure and free energy as well as the related heat capacity and Gruneisen parameter are estimated. The ground-state findings (incomplete order, residual entropy) are similar to those of short-range Potts glasses. A correspondence between density matrix and mean field treatment to the QG problem is also discussed.

2D NMR. Density Matrix and Product Treatment. VonG. D. Mateescu undA. Valeriu. Prentice Hall, Englewood Cliffs, USA, 1993. 250 S., geb. 69.00 $. – ISBN 0-13-013368-X

Angewandte ChemieVolume 107, Issue 1 p. 132-133 Bücher 2D NMR. Density Matrix and Product Treatment. Von G. D. Mateescu und A. Valeriu. Prentice Hall, Englewood Cliffs, USA, 1993. 250 S., geb. 69.00 $. – ISBN 0-13-013368-X James Keeler, James Keeler Department of Chemistry University of Cambridge (Großbritannien)Search for more papers by this author James Keeler, James Keeler Department of Chemistry University of Cambridge (Großbritannien)Search for more papers by this author First published: 5 January 1995 https://doi.org/10.1002/ange.19951070138AboutPDF ToolsRequest permissionAdd to favorites ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume107, Issue15 January 1995Pages 132-133 This is the German version of Angewandte Chemie. Note for articles published since 1962: Do not cite this version alone. Take me to the International Edition version with citable page numbers, DOI, and citation export. We apologize for the inconvenience. RelatedInformation

Full temporal density-matrix treatment of dual wavelength, arbitrary bandwidth, pulsed laser excitation of atoms with degenerate states in high collisional media

A full time-dependent theory, based on the Density-Matrix (D.M.) formalism, for two-step pulsed excitation of atoms in collision-dominated media by pulsed laser light of arbitrary bandwidth is presented. The atoms consist of three levels, of which each one, in turn, can consist of an arbitrary number of degenerate states. The atoms are exposed both to quenching collisions as well as elastic collisions. From a general set of density-matrix equations a more manageable, reduced set of fully time-dependent D.M. equations is formulated (the total number of equations is not more than 10, in contrast to the N 2 equations needed for a general set of D.M. equations, N being the total number of states within all three levels). The following approximations and assumptions have been made: the rotating-wave approximation; all individual transition probabilities between different states within a given pair of levels are the same (implying that the only input parameters for the transition probabilities are the spontaneous emission rates); all coherences between different states within each level are washed out by the high collisional rates; and the laser light is linearly polarized with an arbitrary bandwidth of Lorentzian shape. The full time-dependent equations are then solved in the steady-state limit of the non-diagonal elements, yielding time-dependent rate-equation-like population transfer equations. A few fully time-dependent simulations of some typical cases are given.

Book Review: 2D NMR. Density Matrix and Product Operator Treatment. By G. D. Mateescu and A. Valeriu

Book Review: 2D NMR. Density Matrix and Product Operator Treatment. By G. D. Mateescu and A. Valeriu

Femtosecond polarization spectroscopy: A density matrix description

A density matrix treatment of the time evolution of the third order polarization response describing the optical heterodyne detected (OHD) transient birefringence and dichroism excited by ultrafast pulses is given. The relationship between frequency domain (Raman scattering) and time domain (pump–probe) spectroscopies is revealed by this pathway explicit description. Constructive and destructive interferences between time evolution density matrix pathways account for the respective strong birefringent and weak dichroic ground state nuclear response when the pulses are electronically nonresonant. However, for electronically resonant chromophores, the dichroic response is larger than the corresponding birefringent response due to constructive and destructive interferences respectively between density matrix time evolution histories. No such interferences contribute to spontaneous Raman scattering. The relative magnitude of the resonant dichroic and birefringent responses is pulse width dependent in the fast pulse limit and dependent on the relative rates of optical dephasing and ground state nuclear motion in the rapid optical dephasing limit. The spatial interpretation of the ground and excited state OHD polarization responses is given within the context of this polarization approach and the familiar Maker–Terhune notation. These relationships between time and frequency domain spectroscopies are illustrated by the observed OHD birefringence and dichroism and the spontaneous Raman spectra of both a nonresonant liquid (chloroform) and a resonant solution (I2 in n-hexane).

Generation of impossible cross-peaks between bulk water and biomolecules in solution NMR.

Intermolecular multiple-quantum coherences between bulk water and a glycoprotein fragment at modest concentration (20 mM) have been experimentally produced and detected, although such coherences are inconceivable in the normal theoretical framework of nuclear magnetic resonance. A density matrix treatment explains these results by including the long-range dipolar interaction between spins and by discarding the high-temperature approximation. These results imply that peak intensities (critical for structural determinations) can be distorted in many gradient experiments, and show that magic-angle gradients provide substantial improvements with reduced gradient strengths. They also suggest methods for contrast enhancement in magnetic resonance imaging.

A density-matrix treatment of step-wise laser excitations of atoms with degenerate states in high collisional media

A theory, based on the density-matrix formalism, for two-step excitation of atoms between three levels with arbitrary degeneracies in collision-dominated media by pulsed laser light of arbitrary bandwidth is presented. First, a general set of density-matrix equation is formulated within the rotating-wave approximation for a three level system, in which each level consists of an arbitrary number of sub-states. The system, composed of N 2 equations (where N is the total number of sub-states of the atomic levels involved), is then reduced to six full time-dependent equations by a summation of the diagonal elements for each level and by an averaging of the non-diagonal elements for each transition. The high collisional rates are assumed to wash out all coherence between the sub-states within each level. It is assumed that the laser light is linearly polarized and has a Lorentzian shape (the finite bandwidths of the lasers are included as phase-fluctuations given by the phase-diffusion model). The equations are solved in the steady-state limit of the non-diagonal elements, yielding time dependent rate-equation-like population-transfer equations. An analytical solution in closed form of the full steady-state situation is also given.

Design consideration of miniature OPFIRL. II. Popt of miniature cavity OPFIRL affected by Ro

The influence of the optimum parameters of mini-OPFIRL by the output couple of laser cavity was studied theoretically. The Density Matrix treatment is applied to a three-level system for steady state. The Density Matrix equations were solved under the assumption that Is ⩾ 1E–13 w/cm2 equal to the actual FIR power density at any points in the sample tube. Through numerical calculations, we found that the output coupling of OPFIRL affected seriously the energy exchange between pumping signal and FIR signal the stored energy of FIR signal and the optimum operating gas pressure. These problems are important to design a practical miniature OPFIRL.

Deuterium NMR relaxation studies of peptide-lipid interactions.

A unique model membrane system composed of a synthetic amphiphilic peptide (Lys2-Gly-Leu16-Lys2-Ala-amide) and a specifically labeled phospholipid (1,2-[7,7-2H2]dipalmitoyl-sn-glycero-3-phosphocholine) has been studied by 2H NMR, using inversion recovery, quadrupolar echo, and modified Jeener-Broekaert sequences, from 213 to 333 K, at molar peptide concentrations of 0, 2, 4, and 6%. Analysis of the experiments, employing a density matrix treatment based on the stochastic Liouville equation, revealed information about the dynamic organization of the lipid in the model membrane system, whose phase behavior has been determined previously [Huschilt et al. (1985) Biochemistry 24, 1377-1386]. The dynamic organization is described in terms of segmental and molecular order parameters and in terms of correlation times corresponding to both internal and overall lipid motions. In the liquid crystalline phase, the molecular order parameter, SZZ, was observed to decrease slightly upon addition of peptide while the conformational order parameter corresponding to the seventh segment, SZ'Z', did not change for any concentration of peptide. In general, the gauche-trans isomerization rate in the middle of the chain was not observed to change upon peptide addition, whereas the whole body reorientational correlation times (tau R parallel and tau R perpendicular) increased by nearly an order of magnitude. The anisotropy ratio (tau R perpendicular/tau R parallel) decreased with peptide added. An additional motion which involves a jump about the axis of the sn-2 chain is also observed to be slowed down significantly in the presence of peptide.(ABSTRACT TRUNCATED AT 250 WORDS)