Ramachandran-type plots for glycosidic linkages: Examples from molecular dynamic simulations using the Glycam06 force field

The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran's idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama) plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined by (alpha, phi, psi) and (beta, phi, psi), whereas for three-bond linkages, there are 54 possible regions that can be defined by (alpha, phi, psi, omega) and (beta, phi, psi, omega). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06 force field through comparison to experimental data, and discuss the general trends observed in the plots.     

Numerical simulation of the effect of solvent viscosity on the motions of a beta-peptide heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a beta-peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H-beta3-HVal-beta3-HAla-beta3-HLeu-(S,S)-beta3-HAla(alphaMe)-beta3-HVal-beta3-HAla-beta3-HLeu-OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a beta-peptide on solvent viscosity has two regimes; a result that was observed in another computational study for alpha-peptides.     

Molecular motions and ion diffusions of the room-temperature ionic liquid 1,2-dimethyl-3-propylimidazolium bis(trifluoromethylsulfonyl)amide (DMPImTFSA) studied by 1H, 13C, and 19F NMR

The diffusive properties of an imidazolium room-temperature ionic liquid (RTIL), 1,2-dimethyl-3-propylimidazolium bis(trifluoromethylsulfonyl)amide (DMPImTFSA), are studied from the ionic conductivity and the ion diffusion coefficients measured by pulsed field gradient spin echo NMR. The temperature-dependent (1)H, (19)F, and (13)C NMR spin-lattice relaxation time T(1) values were observed, and the (1)H T(1) for DMPIm showed T(1) minima for various protons. According to the Bloemberger-Purcell-Pound (BPP) equation, the correlation time tau(c) values were directly calculated from (1)H NMR. By using the (1)H tau(c) values, an evaluation of the (13)C T(1) was attempted for the carbons having protons. The tau(c) estimated for molecular motions of DMPIm changes from 1.3 ns at 253 K to 72 ps at 353 K. The Stokes-Einstein-Debye (SED) model suggests that the tau(c) is too short for the overall molecular reorientation near room temperature. Consequently, the possibility of small-angle molecular rotation is proposed and tentative flip angles are calculated by using the translational diffusion coefficient, the bulk viscosity measured in this study, and the tau(c) obtained from (1)H T(1) data in the temperature range between 283 and 353 K. The flip amplitude increases with the temperature. DMPIm has isotropic reorientational motions with temperature-dependent amplitude, in addition to fast intramolecular motions such as methylene segmental motions, methyl rotational motion, and conformational exchange of the imidazolium ring. The existence of fast motions of TFSA is also shown. The translational diffusion of the ions is the slowest dynamic process in the present RTIL. Ab initio molecular orbital calculations are performed to understand the geometries of stable complexes of DMPIm(+) and TFSA(-), and the formation energies from the isolated ions are evaluated. The computed results are important for interpreting the (1)H T(1) behaviors observed for the imidazolium ring protons.     

Vibrational spectra from atomic fluctuations in dynamics simulations. II. Solvent-induced frequency fluctuations at femtosecond time resolution

The midinfrared (MIR) spectra of molecules in polar solvents exhibit inhomogeneously broadened bands whose spectral positions are shifted as compared to the gas phase. The shifts are caused by interactions with structured solvation shells and the broadenings by fluctuations of these interactions. The MIR spectra can be calculated from hybrid molecular dynamics (MD) simulations, which treat the solute molecule by density functional theory and the solvent by molecular mechanics by the so-called instantaneous normal mode analysis (INMA) or by Fourier transforming the time correlation function (FTTCF) of the molecular dipole moment. In Paper I of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12233 (2004)] we explored an alternative method based on generalized virial (GV) frequencies noting, however, that GV systematically underestimates frequencies. As shown by us these artifacts are caused by solvent-induced fluctuations of the (i) equilibrium geometry, (ii) force constants, and (iii) normal mode directions as well as by (iv) diagonal and (v) off-diagonal anharmonicities. Here we now show, by analyzing the time scales of fluctuations and sample MD trajectories of formaldehyde in the gas phase and in water, that all these sources of computational artifacts can be made visible by a Fourier analysis of the normal coordinates. Correspondingly, the error sources (i) and (iii)-(v) can be removed by bandpass filtering, as long as the spectral signatures of the respective effects are well separated from the fundamental band. Furthermore, the artifacts arising from effect (ii) can be strongly diminished by a time-resolved version of the GV approach (TF-GV). The TF-GV method then yields for each mode j a trajectory of the vibrational frequency omega(j)(tmid R:tau) at a time resolution tau>tau(j), which is only limited by the corresponding oscillation time tau(j)=2pi/omega(j) and, thus, is in the femtosecond range. A correlation analysis of these trajectories clearly separates the librational motions from the conformational dynamics of the solvation shells and yields the inhomogeneously broadened MIR spectra, if the theory of motional narrowing is properly included. The MIR spectrum of formaldehyde in solution obtained by TF-GV agrees very well with the FTTCF result, if one applies the so-called "harmonic approximation" quantum correction factor and a temperature scaling to the FTTCF intensities. Also for INMA an excellent agreement is achieved if one disregards a slight INMA overestimate of linewidths.     

Ligand-to-metal charge transfer excited states with unprecedented luminescence yield in fluid solution

A bridged d0 zirconocene dichloride is reported as a first group 4 metal complex possessing rare long-lived ligand-to-metal charge transfer (LMCT) excited states with high emission yields and excited-state lifetimes in fluid solutions (e.g., PhiLUM = 0.41 and tau = 17.6 micros in 1,2-dichlorobenzene at 20 degrees C). The basic emission parameters PhiLUM and tau are shown to be extremely solvent-dependent in fluids at room temperature. The first principle dependences of LMCT emission parameters on solvent properties are revealed with use of the target complex. For fluid solutions, the linear correlation between PhiLUM and tau is reported, thus suggesting that a solvent determines the rate constant for nonradiative decay, knr.     

Triplet formation involving a polar transition state in a well-defined intramolecular perylenediimide dimeric aggregate

A cofacially stacked perylenediimide (PDI) dimer with a xanthene linker was studied under a variety of conditions (solvent, temperature) and serves as a model for the molecular interactions occurring in solid films. Intrinsically, the PDI units have a fluorescence quantum yield (Phi F) close to unity, but Phi F is lowered by a factor of 6-50 at room temperature when two PDI moieties are held in a cofacial arrangement, while the decay time of the most emissive state is increased significantly (tau F = 27 ns in toluene) compared to a monomeric PDI molecule (tau F = 4 ns). Fluorescence measurements show a strong solvent and temperature dependence of the characteristics of the emissive excited state. In a glassy matrix of toluene (TOL) or 2-methyltetrahydrofuran (2-MeTHF), Phi F is high, and the decay time is long (tau F = approximately 50 ns). At higher temperature, both Phi F and tau F are reduced. Interestingly, at room temperature, Phi F and tau F are also reduced with increasing solvent polarity, revealing the presence of a polar transition state. Photoinduced absorption of the stacked molecules from the picosecond to the microsecond time scale shows that after photoexcitation reorganization occurs in the first nanoseconds, followed by intersystem crossing (ISC), producing the triplet excited state. Using singlet oxygen ( (1)Delta g) luminescence as a probe, a triplet quantum yield (Phi T) greater than 50% was obtained in air-saturated 2-Me-THF. Triplet formation is exceptional for PDI chromophores, and the enhanced ISC is explained by a decay involving a highly polar transition state.     

Pathways and populations: stereoelectronic insights into the exocyclic torsion of 5-(hydroxymethyl)tetrahydropyran

High level ab initio computations in vacuum and with the IEFPCM implicit solvent model are carried out on 5-(hydroxymethyl)tetrahydropyran to investigate the effects of water on the exocyclic torsional surface. Rotamer populations evaluated from the omega(C-C-C-O), theta(C-C-C-O) solvent surface agree almost quantitatively with experimental values for the closely related methyl 4-deoxy-alpha-D-xylohexopyranoside. Potentials of mean force obtained from the two surfaces show substantial solvent stabilization of the TG (omega = 180 +/- 60 degrees) rotamer and the barriers at omega= 120 and 240 degrees but solvent destabilization at the cis barrier (omega = 0 degrees). Natural bond orbital analyses indicate that energetics of these effects are largely explained by overstabilization of the vacuum GT (omega= 60 +/- 60 degrees) and GG (omega = 300 +/- 60 degrees) rotamers. Solvent stabilization of theta conformations provides entropic stabilization.     

Mosaic energy landscapes of liquids and the control of protein conformational dynamics by glass-forming solvents

Using recent advances in the Random First-Order Transition (RFOT) Theory of glass-forming liquids, we explain how the molecular motions of a glass-forming solvent distort the protein's boundary and slave some of the protein's conformational motions. Both the length and time scales of the solvent imposed constraints are provided by the RFOT theory. Comparison of the protein relaxation rate to that of the solvent provides an explicit lower bound on the size of the conformational space explored by the protein relaxation. Experimental measurements of slaving of myoglobin motions indicate that a major fraction of functionally important motions have significant entropic barriers.     

Numerical Simulation of the Effect of Solvent Viscosity on the Motions of a β‐Peptide Heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a β‐peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐(S,S)‐β³‐HAla(αMe)‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a β‐peptide on solvent viscosity has two regimes; a result that was observed in another computational study for α‐peptides.     

Extreme fluorescence sensitivity of some aniline derivatives to aqueous and nonaqueous environments: mechanistic study and its implication as a fluorescent probe

Effects of solvent water on the photophysical properties of a series of meta- and para-substituted anilines have been investigated by means of time-resolved fluorescence, transient absorption, and photoacoustic measurements. Some aniline derivatives exhibit extremely short fluorescence lifetime (tau(f)) and small quantum yield (Phi(f)) in water (e.g., tau(f) = 45 ps and Phi(f) = 0.0019 for m-cyanoaniline (m-ANCN) in H(2)O), which is in marked contrast with their much larger values in nonaqueous solvents (tau(f) = 7.3 ns and Phi(f) = 0.14 for m-ANCN in acetonitrile). Photoacoustic and transient absorption measurements show that the remarkable fluorescence quenching of m-ANCN in water is attributed almost exclusively to fast internal conversion. The lifetime measurements of m-ANCN in H(2)O/acetonitrile binary solvent mixtures reveal that the quenching is related to variation of hydrogen-bonding interactions between the amino group and water molecules and the conformational change of the amino group upon electronic excitation. Similar fluorescence quenching due to solvent water is also found for N-alkylated m-ANCNs. The drastic differences in the fluorescence intensity and lifetime of m-ANCNs under hydrophobic and hydrophilic environments and also the large solvent polarity dependence of the fluorescence band position suggest the possibility that they can be utilized as fluorescent probes for investigating the microenvironment of biological systems. In suspensions of human serum albumin (HSA) in water, remarkable enhancement of the fluorescence intensity and lifetime is observed for m-ANCN and its N-alkylated derivatives, demonstrating that m-ANCNs can be a candidate for novel fluorescent probe with small molecular size.     

Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. II. Electron dynamics and outer ionization of the nanoplasma

We explore electron dynamics in molecular (CD4)(1061) clusters and elemental Xen (n=249-2171) clusters, responding to ultraintense (intensity I=10(16)-10(19) W cm(-2)) laser fields. Molecular dynamics simulations (including magnetic field and relativistic effects) and analyses of high-energy electron dynamics and nuclear ion dynamics in a cluster interacting with a Gaussian shaped laser field (frequency 0.35 fs(-1), photon energy 1.44 eV, phase 0, temporal width 25 fs) elucidated the time dependence of inner ionization, the formation of a nanoplasma of unbound electrons within the cluster or its vicinity, and of outer ionization. We determined the cluster size and the laser intensity dependence of these three sequential-parallel electronic processes. The characteristic times for cluster inner ionization (tau(ii)) and for outer ionization (tau(oi)) fall in the femtosecond time domain, i.e., tau(ii)=2-9 fs and tau(oi)=4-15 fs for (CD4)(1061), tau(ii)=7-30 fs and tau(oi)=5-13 fs for Xe(n) (n=479,1061), with both tau(ii) and tau(oi) decreasing with increasing I, in accord with the barrier suppression ionization mechanism for inner ionization of the constituents and the cluster barrier suppression ionization mechanism for outer ionization. The positive delay times Deltatau(OI) between outer and inner ionization (e.g., Deltatau(OI)=6.5 fs for Xen at I=10(16) W cm(-2) and Deltatau(OI)=0.2 fs for (CD4)(1061) at I=10(19) W cm(-2)) demonstrate that the outer/inner ionization processes are sequential. For (CD4)(1061), tau(ii)tau(oi), reflecting on the energetic hierarchy in the ionization of the Xe atoms. Quasiresonance contributions to the outer ionization of the nanoplasma were established, as manifested in the temporal oscillations in the inner/outer ionization levels, and in the center of mass of the nanoplasma electrons. The formation characteristics, dynamics, and response of the nanoplasma in molecular or elemental clusters were addressed. The nanoplasma is positively charged, with a high-average electron density [rho(P)=(2-3)10(22) cm(-3)], being characterized by high-average electron energies epsilon(av) (e.g., in Xe(1061) clusters epsilon(av)=54 eV at I=10(16) W cm(-2) and epsilon(av)=0.56-0.37 keV at I=10(18) W cm(-2), with epsilon(av) proportional, variant I(1/2)). Beyond the cluster boundary the average electron energy markedly increases, reaching electron energies in the range of 1.2-40 keV for outer ionization of Xe(n) (n=249-2171) clusters. The nanoplasma exhibits spatial inhomogeneity and angular anisotropy induced by the laser field. Femtosecond time scales are predicted for the nanoplasma production (rise times 7-3 fs), for the decay (decay times approximately 5 fs), and for the persistence time (30-10 fs) of a transient nanoplasma at I=10(17)-10(18) W cm(-2). At lower intensities of I=10(16) W cm(-2) a persistent nanoplasma with a "long" lifetime of > 50 fs will prevail.     

Hydrogen bond breaking dynamics of the water trimer in the translational and librational band region of liquid water.

The effect of exciting each of the three classes of intermolecular vibrations on the hydrogen bond lifetime (tau(H)) of the isolated water trimer is investigated by far-infrared laser spectroscopy. Single excitation of a librational vibration decreases tau(H) by 3 orders of magnitude to tau(H) = 1-6 ps, comparable to the time scale of a number of important bulk water dynamical relaxation processes. In contrast, excitation of translational or torsional vibrations has no significant effect (tau(H) = 1-2 ns). Although such a dependence of tau(H) on intermolecular motions has also been proposed for liquid water via computer simulations, these are the first experiments that provide a detailed molecular picture of the respective motions without extensive interpretation.     

Simulation studies of ionic liquids: orientational correlations and static dielectric properties

The ionic liquids BMIM+I-, BMIM+BF4-, and BMIM+PF6- were simulated by means of the molecular dynamics method over a time period of more than 100 ns. Besides the common structural analysis, e.g., radial distribution functions and three dimensional occupancy plots, a more sophisticated orientational analysis was performed. The angular correlation functions g(00)110(r) and g(00)101(r) are the first distance dependent coefficients of the pairwise orientational distribution function g(rij,Omega1,Omega2,Omega12). These functions help to interpret the three dimensional plot and reveal interesting insights into the local structure of the analyzed ionic liquids. Furthermore, the collective network of ionic liquids can be characterized by the Kirkwood factor Gkappa(r) [J. Chem. Phys. 7, 911 (1939)]. The short-range behavior (r<10 A) of this factor may be suitable to predict the water miscibility of the ionic liquid. The long-range limit of Gkinfinity is below 1 which demonstrates the strongly coupled nature of the ionic liquid networks. In addition, this factor relates the orientational structure and the dielectric properties of the ionic liquids. The static dielectric constant epsilon(omega=0) for the simulated system is 8.9-9.5. Since in ionic liquids the very same molecule contributes to the total dipole moment as well as carries a net charge, a small, but significant contribution of the cross term between the total dipole moment and the electric current to epsilon(omega=0) is observed.     

Hydration and temperature interdependence of protein picosecond dynamics

We investigate the nature of the solvent motions giving rise to the rapid temperature dependence of protein picoseconds motions at 220 K, often referred to as the protein dynamical transition. The interdependence of picoseconds dynamics on hydration and temperature is examined using terahertz time domain spectroscopy to measure the complex permittivity in the 0.2-2.0 THz range for myoglobin. Both the real and imaginary parts of the permittivity over the frequency range measured have a strong temperature dependence at >0.27 h (g water per g protein), however the permittivity change is strongest for frequencies <1 THz. The temperature dependence of the real part of the permittivity is not consistent with the relaxational response of the bound water, and may reflect the low frequency protein structural vibrations slaved to the solvent excitations. The hydration necessary to observe the dynamical transition is found to be frequency dependent, with a critical hydration of 0.19 h for frequencies >1 THz, and 0.27 h for frequencies <1 THz. The data are consistent with the dynamical transition solvent fluctuations requiring only clusters of ~5 water molecules, whereas the enhancement of lowest frequency motions requires a fully spanning water network.     

Solvation shell dynamics studied by molecular dynamics simulation in relation to the translational and rotational dynamics of supercritical water and benzene

The solvation shell dynamics of supercritical water is analyzed by molecular dynamics simulation with emphasis on its relationship to the translational and rotational dynamics. The relaxation times of the solvation number (tau S), the velocity autocorrelation function (tau D), the angular momentum correlation function (tau J), and the second-order reorientational correlation function (tau 2R) are studied at a supercritical temperature of 400 degrees C over a wide density region of 0.01-1.5 g cm(-3). The relaxation times are decomposed into those conditioned by the solvation number n, and the effect of the short-ranged structure is examined in terms of its probability Pn of occurrence. In the low to medium-density range of 0.01-0.4 g cm(-3), the time scales of water dynamics are in the following sequence: tau D>tau S approximately or > tau J approximately or > tau 2R. This means that the rotation in supercritical water is of the "in-shell" type while the translational diffusion is not. The comparison to supercritical benzene is also performed and the effect of hydrogen bonding is examined. The water diffusion is not of the in-shell type up to the ambient density of 1.0 g cm(-3), which corresponds to the absence of the transition from the collision to the Brownian picture, whereas such transition is present in the case of benzene. The absence of the transition in water comes from the fast reorganization of the hydrogen bonds and the enhanced mobility of the solvation shell in supercritical conditions.     

Regulation of folding and photochromic reactivity of terarylenes through a host-guest interaction

The photochromic reactivity of terarylenes is integrated with molecular folding that is controlled through a host-guest interaction. A thieno[3,2,b]pyridine unit is introduced into a photochromic terarylene structure as an aryl unit to form a guest-interacting site. Thienopyridine-containing terarylenes showed solvent-dependent photochromic reactivity in solution. A terarylene moiety that contains two thienopyridyl units showed significantly high photocoloration reactivity as high as 88% of photocyclization quantum yield in methanol, whereas that value was only 24% in hexane. A temperature-dependent (1)H NMR spectroscopic study in different solvents indicated an interconversion between photochromic-reactive and unreactive conformations. In methanol, the intermolecular interaction between terarylene species and the solvent molecule slows the rate of interconversion and increases the population of the photochromic-active form, whereas the unreactive conformation is dominant in hexane. Crystal-structural studies demonstrated the perfect regulation of molecular folding between a photochromic-active form and an unreactive conformation by changing the solvents for recrystallization. Single crystals prepared from solutions in methanol showed reversible photochromic reactivity, whereas recrystallization from solutions in hexane did not show this reactivity. X-ray crystallographic studies of single crystals from solutions in methanol demonstrated that the photochromic molecules bind a solvent methanol molecule at the guest-interacting site to regulate the molecular conformation into a photochromic-active form in collaboration with specific intramolecular interactions, whereas crystals from solutions in hexane possess the photochromic-unreactive conformation.     

Ultrafast relaxation dynamics of perchlorinated cycloheptatriene in solution

The photochemistry of perchlorinated cycloheptatriene (CHTCl(8)) has been studied by means of ultrafast pump-probe, transient anisotropy and continuous UV-irradiation experiments in various solvents as well as by DFT calculations. After UV-excitation to the 1A' '-state, two competing reactions occur--a [1,7]-sigmatropic chlorine migration via two ultrafast internal conversions and a [4,5]-electrocyclization forming octachlorobicylo[3.2.0]hepta-[2,6]-diene. The first reaction has been studied by excitation with a 263 nm femtosecond-laser pulse. Pump-probe experiments reveal a first, solvent-independent time constant, tau1(CHTCl(8)) = 140 fs, that can be associated with the electronic relaxation of the 2A'-1A' ' transition, while a second one, tau2(CHTCl(8)), ranges from 0.9 to 1.8 ps depending on the polarity of the solvent. This finding is consistent with a [1,7]-chlorine migration during the 1A'-2A' transition where the migrating chlorine atom is partly negatively charged. The charge separation has also been confirmed by DFT calculations. Transient anisotropy measurements result in a time zero value of r(0) = 0.35 after deconvolution and a decay constant of tau1(a) = 120 fs, which can be explained by vibrational motions of CHTCl(8) in the electronically excited states, 1A' ' and 2A'. After continuous UV-irradiation of CHTCl(8), octachlorobicylo[3.2.0]hepta-[2,6]-diene is primarily formed with a solvent-dependent yield. From these investigations, we suggest a relaxation mechanism for CHTCl(8) after photoexcitation that is comparable to cycloheptatriene.     

Electrospray ionization/atmospheric pressure photoionization multimode source for low-flow liquid chromatography/mass spectrometric analysis

Analysis of several polar and non-polar compounds is performed with a newly developed dual electrospray ionization/atmospheric pressure photoionization (ESI/APPI) or ESPI source. Several variables are considered in the source, such as ESI probe heater temperature, solvent flow, dopant effects, repeller plate voltage, source geometry and photon energy (Kr vs. Ar lamp). Direct photoionization resulting in a molecular radical cation [M](*+) dominates at high temperatures (>400 degrees C) and low flow rates (<200 microL/min). Indirect photo-induced chemical ionization (PCI) involving solvent molecules becomes important at lower temperatures and higher solvent flow rates. Indirect PCI is enhanced using an Ar lamp, which yields comparable [M+H](+) signal but poorer [M](*+) signal than the Kr lamp at lower temperatures and higher flow rates. This is in support of our recent finding that the Ar lamp results in a solvent-dependent enhancement of analyte molecules via PCI. Analysis of 12 compounds in methanol under low-flow conditions (10 microL/min) demonstrates that the dual ESPI source performs favorably for most compounds versus the standard ESCI source, and significantly better than ESCI for the analysis of unstable drugs, like flurbiprofen. Several factors contributing to the benefits of the ESPI source are the shared optimal geometry for ESI and APPI sources and soft ionization of APPI versus APCI.     

Markovian approximation in the relaxation of open quantum systems

In this paper, we examine the validity of the Markovian approximation and the slippage scheme used to incorporate short time transient memory effects in the Markovian master equations (Redfield equations). We argue that for a bath described by a spectral function, J(omega), that is dense and smoothly spread out over the range omega(d), a time scale of tau(b) approximately 1/omega(d) exists; for times of t > tau(b), the Markovian approximation is applicable. In addition, if J(omega) decays to zero reasonably fast in both the omega --> 0 and omega --> infinity limits, then the bath relaxation time, tau(b), is determined by the width of the spectral function and is weakly dependent on the temperature of the bath. On the basis of this criterion of tau(b), a scheme to incorporate transient memory effects in the Markovian master equation is suggested. Instead of using slipped initial conditions, we propose a concatenation scheme that uses the second-order perturbation theory for short time dynamics and the Markovian master equation at long times. Application of this concatenation scheme to the spin-boson model shows that it reproduces the reduced dynamics obtained from the non-Markovian master equation for all parameters studied, while the simple slippage scheme breaks down at high temperatures.