Density-matrix Calculations Research Articles

3D RINEPT {1H}‐31P CSI: A feasible approach for the study of membrane turnover in the human brain

A fast, full 3D elliptical k-space encoding phosphorous-31 ((31)P) chemical shift imaging sequence, incorporating heteronuclear polarization transfer editing (RINEPT), was established. RINEPT literally requires simultaneous pulses at the frequencies of both the sensitive and the insensitive nuclei, but only a few MR imaging systems feature a second independent transmit channel. In this study, possible signal degradation of a sequential sequence design on systems featuring a single transmit channel was investigated with spin density matrix calculations and phantom measurements. In addition, metabolite signal intensities were determined in vivo as a function of echo and repetition times. The results enable optimization of the signal-to-noise ratio of one or more metabolites of interest. The results convincingly show that the optimized RINEPT sequence is useful in clinical routine (31)PMRS protocols and provides spectra of excellent quality for the study of cell membrane phospholipid turnover in the human brain even at a low field strength of 1.5T. The 3D sequence design allows covering the whole brain in a single measurement, while scan times are compliant with clinical routine protocols.

Direct determination of ultrafast intersubband hole relaxation times in voltage biased SiGe quantum wells by a density matrix interpretation of femtosecond resolved photocurrent experiments

We report the quantitative and direct determination of hole intersubband relaxation times in a voltage biased SiGe heterostructure using density matrix calculations applied to a four-level system in order to interpret photocurrent (PC) pump–pump experiments. One consistent set of parameters allows the simulation of two kinds of experiments, namely pump–pump photocurrent experiments at a free electron laser (wavelength 7.9 μm) and the laser-power dependence of the PC signal. This strongly confirms the high reliability of these parameter values, of which the most interesting in respect to Si based quantum cascade laser development is the extracted heavy-hole relaxation time. The simulations show that this relaxation time directly determines the experimentally observed decay of the pump–pump photocurrent signal as a function of the delay time. For a heavy hole intersubband spacing of 160 meV, a value of 550 fs was obtained. The experimental method was further applied to determine the LH1–HH1 relaxation time of a second sample with a transition energy below the optical phonon energy. The observed relaxation time of 16 ps is consistent with the value found for the same structure by transmission pump–probe experiments.

Electron sharing indexes at the correlated level. Application to aromaticity calculations

Electron sharing indexes (ESI) have been applied to numerous bonding situations to provide an insight into the nature of the molecular electronic structures. Some of the most popular ESI given in the literature, namely, the delocalization index (DI), defined in the context of the quantum theory of atoms in molecules (QTAIM), and the Fuzzy-Atom bond order (FBO), are here calculated at a correlated level for a wide set of molecules. Both approaches are based on the same quantity, the exchange-correlation density, to recover the electron sharing extent, and their differences lie in the definition of an atom in a molecule. In addition, while FBO atomic regions enable accurate and fast integrations, QTAIM definition of an atom leads to atomic domains that occasionally make the integration over these ones rather cumbersome. Besides, when working with a many-body wavefunction one can decide whether to calculate the ESI from first-order density matrices, or from second-order ones. The former way is usually preferred, since it avoids the calculation of the second-order density matrix, which is difficult to handle. Results from both definitions are discussed. Although these indexes are quite similar in their definition and give similar descriptions, when analyzed in greater detail, they reproduce different features of the bonding. In this manuscript DI is shown to explain certain bonding situations that FBO fails to cope with. Finally, these indexes are applied to the description of the aromaticity, through the aromatic fluctuation (FLU) and the para-DI (PDI) indexes. FLU and PDI indexes have been successfully applied using the DI measures, but other ESI based on other partitions such as Fuzzy-Atom can be used. The results provided in this manuscript for carbon skeleton molecules encourage the use of FBO for FLU and PDI indexes even at the correlated level.

Nonlinear magneto-optical rotation with modulated light in tilted magnetic fields

Larmor precession of laser-polarized atoms contained in anti-relaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR) is a promising technique for a new generation of ultra-sensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency- or amplitude-modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. New NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These new resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method for NMOR-based vector magnetometry.

Classical description of the dynamics and time-resolved spectroscopy of nonadiabatic cis– trans photoisomerization

The mapping formulation of nonadiabatic quantum dynamics is applied to obtain a classical description of the ultrafast dynamics and time-resolved spectroscopy of a photochemical reaction. Adopting a previously studied dissipative two-state two-mode model of nonadiabatic cis–trans photoisomerization, classical mapping simulations are compared to quantum-mechanical reduced density matrix calculations. Overall, the simple classical method is found to reproduce the quantum reference calculations quite well. In particular, it is studied if the classical approach yields the correct long-time cis/trans localization of the wave packet and therefore the correct quantum yield of the photoreaction. As the long-time behavior of the classical mapping formulation suffers from the well-known zero point energy problem of classical mechanics, a new practical method is proposed to determine a zero point energy correction. Employing a second-order Franck–Condon-type approximation, the capability of the classical method to simulate time- and frequency-resolved pump–probe spectra of the nonadiabatic photoreaction is studied. The potential of the classical approach as a practical method to describe condensed-phase photoreactions is discussed.

Optical pumping and coherence effects in fluorescence from a four level system

An effective four-level system around the D2 line of 85Rb at room temperature, is experimentally investigated by fluorescent studies under the action of two driving fields L1 and L2. This system exhibits unique features in fluorescence as a function of frequency separation between L1 and L2. In particular, at two-photon resonance, when the Rabi frequency of L1 exceeds that of L2, signatures of Electromagnetically Induced Transperancy effect (EIT) arising from the three-level Λ sub-system is present as a sub-natural dip in fluorescence from the fourth level. At comparable strengths of L1 and L2 the fluorescence features indicate a regime, where the effects arising from optical pumping and EIT effect due to ground hyperfine level coherence coexist. We see in the coexistence regime, saturation effects arising from difference frequency crossing (DFC) resonances and optical pumping around the EIT window. At low strengths of L1, all signs of coherence vanishes from the system and the fluorescent features result from incoherent optical pumping through the Autler-Townes split states of the excited state hyperfine levels, which are split due to the stronger L2 laser. The dominant role of the L1 laser in creating a robust transparency signal even in the presence of an off-resonant excitation is brought out. The results are supported by density matrix calculations.

Investigation of Tetrahedral Mixed-Metal Carbonyl Clusters by Two-Dimensional 59Co COSY and DQFCOSY NMR Experiments

Two-dimensional (2D) 59Co correlation spectroscopy (COSY)/double-quantum-filtered (DQF)COSY experiments are reported for three tetrahedral mixed-metal clusters HFeCo3(CO)11L with L = PPh3, P(OMe)3, and PCy3 (Cy = cyclohexyl) in which the L-substituted Co center is chemically different from the other two. The 2D 59Co COSY and DQFCOSY NMR spectra of these clusters in solution prove the existence of a scalar coupling constant between the 59Co nuclei. To determine this value for each cluster, 2D 59Co COSY and DQFCOSY NMR spectra have been simulated by numerical density-matrix calculations. The predicted spectra mimic well the features of the experimental spectra if a scalar coupling is introduced between the Co nuclei. It was initially observed that the scalar coupling constants between the Co nuclei obtained from the 2D COSY and DQFCOSY NMR spectra differed significantly. In contrast to the 2D COSY spectra, the diagonal and cross peaks are of comparable intensity in the 2D DQFCOSY spectra, which leads to a considerable increase in the accuracy of the determination of the scalar coupling constant.

Density-matrix calculation of surface-enhanced Raman scattering for p-mercaptoaniline on silver nanoshells

A theoretical analysis of recent experiments measuring the 782 nm surface-enhanced Raman scattering of p-mercaptoaniline bound to silver nanoshells of different core and shell radii [J. B. Jackson and N. J. Halas, Proc. Natl. Acad. Sci. U.S.A. 101, 17930 (2004)] is performed. Electronic structure Hartree-Fock and density-functional theory calculations for Ag salts of p-mercaptoaniline are used to characterize observed vibrational modes and configuration-interaction singles calculations are carried out to examine excited states. Multimode vibronic density-matrix calculations are then made including one excited electronic state, using a classical description of the strong local fields and a phenomenological treatment of relaxations. The spectral behavior as a function of both nanoshell surface-plasmon resonance position and molecular electronic spacing is examined.

A scheme for ultrashort X-ray lasing without inversion

A scheme for obtaining a laser without inversion in the deep X-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in the Ar8+ system. In this system, conventional lasing with population inversion in a neonlike scheme is used. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. The ground level is incoherently pumped into the highest level, while the latter is incoherently depumped into the ground level, at a different adjustable rate. A detailed density matrix calculation of the ladder configuration is performed [3], and the conditions under which the system exhibits inversionless gain, as well as regular gain, are derived. Numerical calculations in the bare state picture exhibits gain without inversion both at resonance and at the generalized Rabi side bands. The probe lineshape is shown to be constructed of two symmetrical dispersionlike features each centered at the generalized Rabi side bands. This is evidence of the quantum interference occurring at these locations and the basis for the gain without inversion.

Proton‐observed carbon‐edited NMR spectroscopy in strongly coupled second‐order spin systems

Proton-observed carbon-edited (POCE) NMR spectroscopy is commonly used to measure 13C labeling with higher sensitivity compared to direct 13C NMR spectroscopy, at the expense of spectral resolution. For weakly coupled first-order spin systems, the multiplet signal at a specific proton chemical shift in POCE spectra directly reflects 13C enrichment of the carbon attached to this proton. The present study demonstrates that this is not necessarily the case for strongly coupled second-order spin systems. In such cases NMR signals can be detected in the POCE spectra even at chemical shifts corresponding to protons bound to 12C. This effect is demonstrated theoretically with density matrix calculations and simulations, and experimentally with measured POCE spectra of [3-13C]glutamate.

Density matrix calculations of gaseous and adsorbate dynamics in electronically excited molecular systems

AbstractThis contribution deals with two approaches for localized phenomena in excited many‐atom systems. The first approach develops a quantum quasi‐classical treatment for the density operator, including all atoms. It is based on a partial Wigner representation and is illustrated with applications to photodissociation of NaI, and to light emission of excited Li interacting with a He cluster. This second application describes the direct dynamics with a time‐dependent electronic density matrix, expanded in a basis set of atomic functions. It shows that such an approach can deal with electronically excited many‐atom systems involving tens of quantum states and hundreds of classical variables. The second approach makes use of the reduced density operator description for a system in a medium. This allows for dissipative dynamics, which can be instantaneous or delayed. An application is presented for femtosecond photodesorption using a Markovian dissipation and construction of the density operator from density amplitudes, for CO/Cu(001). A second application of a reduced density operator has been made to vibrational relaxation of adsorbates, solving integrodifferential equations to compare delayed, instantaneous, and Markovian dissipation. It is concluded that delayed dissipation is needed at short times and that a Markovian treatment is suitable for the interpretation of cross‐sectional measurements that involve long‐term dynamics. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

14N pulsed nuclear quadrupole resonance. 1. Nutation experiments in the case of an axially symmetric electric field gradient tensor

An exact theory based on density matrix calculations is provided for assessing the nuclear quadrupole resonance (NQR) behaviour of a spin 1 (14N) subjected to a single radio-frequency pulse. It concerns a powder sample in zero magnetic field with the assumption of an axially symmetric electric field gradient tensor. Theoretical results, in terms of signal evolution as a function of the pulse length (nutation experiments), are checked against values of the radio-frequency field amplitude provided by NMR measurements performed with the same equipment. Good agreement between theory and experiment is obtained.

A novel extremely localized molecular orbitals based technique for the one-electron density matrix computation

The ‘nearsightedness’ of electronic structure is an underlying principle in many of the linear scaling methods recently developed to study large systems. Among them, there are strategies based on the transfer of orbitals strictly localized on molecular fragments, such as the extremely localized molecular orbitals (ELMOs). Unfortunately, due to the non-orthogonal nature of these orbitals, the density matrix calculation is computationally demanding, so preventing a straightforward application to very large molecules. In this Letter, we show how this problem can be overcome by a proper application of the ‘Divide and Conquer’ strategy to the ELMO approach.

Surface-enhanced Raman scattering and fluorescence near metal nanoparticles

We present a general model study of surface-enhanced resonant Raman scattering and fluorescence, focusing on the interplay between electromagnetic (EM) effects and the molecular dynamics as treated by a density matrix calculation. The model molecule has two electronic levels, is affected by radiative and non-radiative damping mechanisms, and a Franck-Condon mechanism yields electron-vibration coupling. The coupling between the molecule and the electromagnetic field is enhanced by placing it between two Ag nanoparticles. The results show that the Raman scattering cross section can, for realistic parameter values, increase by some 10 orders of magnitude (to $\sim10^{-14}$ cm$^2$) compared with the free-space case. Also the fluorescence cross section grows with increasing EM enhancement, however, at a slower rate, and this increase eventually stalls when non-radiative decay processes become important. Finally, we find that anti-Stokes Raman scattering is possible with strong incident laser intensities, $\sim 1$ mW/$\mu$m.

Optimal timing for in vivo 1H‐MR spectroscopic imaging of the human prostate at 3T

Proton MR spectroscopic imaging ((1)H-MRSI) of the human prostate, which has an interesting clinical potential, may be improved by increasing the magnetic field strength from 1.5T to 3T. Both theoretical and practical considerations are necessary to optimize the pulse timing for spectroscopic imaging of the human prostate at 3T. For in vivo detection of the strongly coupled spin system of citrate, not only should the spectral shape of the signal be easy to identify, but the timing used should produce MR signals at reasonably short echo times (TEs). In this study the spectral shape of the methylene protons of citrate was simulated with density matrix calculations and checked with phantom measurements. Different calculated optimal spectral shapes were measured in patients with prostate cancer with a 2D spectroscopic imaging sequence. T(1) and T(2) relaxation times were calculated for citrate and choline, the two major metabolites of interest in the prostate. We conclude that the optimum timing for in vivo point-resolved spectroscopy (PRESS) imaging at 3T is an interpulse timing sequence of 90 degrees-25 ms-180 degrees- 37.5 ms-180 degrees-12.5 ms-echo. A short repetition time (TR) of 750 ms partially saturates choline signals, but increases the SNR per unit time for citrate, and accommodates a maximum number of weighted averages of an elliptically sampled k-space for accurate localization and minimal contamination of the individual spectra. This is illustrated by means of a 3D spectroscopic imaging experiment in a complete prostate in vivo.

Photodissociation dynamics from quantum–classical density matrix calculations

Photodissociation phenomena are described within a quantum–classical treatment based on the partial Wigner transform of the density matrix and its Liouville–von Neumann equation. Two basic approximations are introduced, to convert the equations into forms readily integrable by numerical methods. Results are presented for the NaI femtosecond time evolution of quantum populations, coherence, position and momenta averages and their dispersion, and for the time evolution of a grid of points in phase space corresponding to a bundle of trajectories. Comparing with exact results, it is concluded that the procedure gives correct results over long times, and properly accounts for the coupling of very different (quasibound and nearly free) atomic motions.

Fluorescence from doubly driven four-level atoms

The unusually narrow features in the fluorescence from 85Rb driven by two laser fields L1 and L2, reported in [1], are explained on the basis of a four-level density matrix calculation. The L2 laser enables atom transfer to the fluorescing levels connected by the strong L1 laser. In turn the L1 laser causes the Autler-Townes splitting of the upper levels connected by L2 laser. These two effects are shown to maximise fluorescence within a narrow spectral range of the scanned L2 laser due to velocity selection of atoms from co-propagating and counter propagating L1 and L2 lasers. The analysis reveals the existence of narrow spectral features from a collection of atoms at room temperature even in the absence of induced coherences between the levels.

Quantum interference effects on the probe amplification without and with inversion in a four-level system

A four-level system driven by two coherent fields is considered. It is shown that in the presence of an incoherent pump, the probe gain at a short wavelength can be achieved due to the quantum interference. Our density matrix calculation provides the conditions for probe amplification from different origins, including gain without population inversion on any state basis, gain with population inversion on the dressed-state basis and gain with population inversion on the bare-state basis. Also, by controlling the Rabi frequency of the coupling field a total change from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.

Interatomic Distance Measurement in Solid-State NMR between a Spin-1/2 and a Spin-5/2 Using a Universal REAPDOR Curve

A universal curve for the solid-state NMR REAPDOR experiment on an isolated spin-1/2-spin-5/2 pair is proposed that provides a simple means to measure their interatomic distance. REAPDOR data were obtained at three separate REAPDOR experiments using different values of the rotor spinning frequency. All points were fitted simultaneously to the universal formula without a need for full density matrix calculations. The 13C-17O distance of 2.45 A was measured between the C6 carbon and the 17O label in a tyrosine sample. The error of 8% in the dipolar coupling (Dfit = 278 Hz) is well within the 15% theoretical tolerance of this curve.

Two-particle density matrix calculation for atom by modified perturbation theory

The two-particle density matrix of hydrogen atoms moving in a solid film is calculated. The probability of surviving a bound state between electron and proton in the course of the atomic motion in the film is discussed. The surviving fraction of the initial beam possesses the increased energy of the Coulomb attraction and lowered energy losses. This fraction can be responsible for the observed number of Rydberg states in the exit beam.