Volume 140, Issue 23, 21 June 2014

We present a new, nucleotidelevel model for RNA, oxRNA, based on the coarsegraining methodology recently developed for the oxDNA model of DNA. The model is designed to reproduce structural, mechanical, and thermodynamic properties of RNA, and the coarsegraining level aims to retain the relevant physics for RNA hybridization and the structure of single and doublestranded RNA. In order to explore its strengths and weaknesses, we test the model in a range of nanotechnological and biological settings. Applications explored include the folding thermodynamics of a pseudoknot, the formation of a kissing loop complex, the structure of a hexagonal RNA nanoring, and the unzipping of a hairpin motif. We argue that the model can be used for efficient simulations of the structure of systems with thousands of base pairs, and for the assembly of systems of up to hundreds of base pairs. The source code implementing the model is released for public use.
 COMMUNICATIONS


Communication: Direct measurements of nascent O(^{3}P_{0,1,2}) finestructure distributions and branching ratios of correlated spinorbit resolved product channels CO(ã ^{3}Π; v) + O(^{3}P_{0,1,2}) and CO(; v) + O(^{3}P_{0,1,2}) in VUV photodissociation of CO_{2}
View Description Hide DescriptionWe present a generally applicable experimental method for the direct measurement of nascent spinorbit state distributions of atomic photofragments based on the detection of vacuum ultraviolet (VUV)excited autoionizingRydberg (VUVEAR) states. The incorporation of this VUVEAR method in the application of the newly established VUVVUV laser velocitymapimagingphotoion (VMIPI) apparatus has made possible the branching ratio measurement for correlated spinorbit state resolved product channels, CO(ã ^{3}Π; v) + O(^{3}P0,1,2) and CO( ; v) + O(^{3}P0,1,2), formed by VUV photoexcitation of CO2 to the 4s(10 ^{1}) Rydberg state at 97,955.7 cm^{−1}. The total kinetic energy release (TKER) spectra obtained from the O^{+} VMIPI images of O(^{3}P0,1,2) reveal the formation of correlated CO(ã ^{3}Π; v = 0–2) with wellresolved v = 0–2 vibrational bands. This observation shows that the dissociation of CO2 to form the spinallowed CO(ã ^{3}Π; v = 0–2) + O(^{3}P0,1,2) channel has no potential energy barrier. The TKER spectra for the spinforbidden CO( ; v) + O(^{3}P0,1,2) channel were found to exhibit broad profiles, indicative of the formation of a broad range of rovibrational states of CO( ) with significant vibrational populations for v = 18–26. While the VMIPI images for the CO(ã ^{3}Π; v = 0–2) + O(^{3}P0,1,2) channel are anisotropic, indicating that the predissociation of CO2 4s(10 ^{1}) occurs via a near linear configuration in a time scale shorter than the rotational period, the angular distributions for the CO( ; v) + O(^{3}P0,1,2) channel are close to isotropic, revealing a slower predissociation process, which possibly occurs on a triplet surface via an intersystem crossing mechanism.

Communication: Direct comparison between theory and experiment for correlated angular and productstate distributions of the groundstate and stretchingexcited O(^{3}P) + CH_{4} reactions
View Description Hide DescriptionMotivated by a recent experiment [H. Pan and K. Liu, J. Chem. Phys.140, 191101 (2014)], we report a quasiclassical trajectory study of the O(^{3}P) + CH4(v k = 0, 1) → OH + CH3 [k = 1 and 3] reactions on an ab initio potential energy surface. The computed angular distributions and cross sections correlated to the OH(v = 0, 1) + CH3(v = 0) coincident product states can be directly compared to experiment for O + CH4(v 3 = 0, 1). Both theory and experiment show that the groundstate reaction is backward scattered, whereas the angular distributions shift toward sideways and forward directions upon antisymmetric stretching (v 3) excitation of the reactant. Theory predicts similar behavior for the O + CH4(v 1 = 1) reaction. The simulations show that stretching excitation enhances the reaction up to about 15 kcal/mol collision energy, whereas the O + CH4(v k = 1) reactions produce smaller cross sections for OH(v = 1) + CH3(v = 0) than those of O + CH4(v = 0) → OH(v = 0) + CH3(v = 0). The former finding agrees with experiment and the latter awaits for confirmation. The computed cold OH rotational distributions of O + CH4(v = 0) are in good agreement with experiment.

Communication: Ultrafast homonuclear correlation spectroscopy with diagonal suppression^{a)}
View Description Hide DescriptionA novel ultrafast 2D NMR experiment is introduced for homonuclear correlation spectroscopy in solution state, with diagonal peak suppression in each scan of a two scan procedure. This experiment permits clear visualization of cross peaks between spins whose chemical shifts are very close, which could otherwise be masked by diagonal peaks. The present report describes the principles of its design and illustrates actual performance.
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 ARTICLES

 Theoretical Methods and Algorithms

Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues
View Description Hide DescriptionWe developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.N. Roy, J. Phys. Chem. A117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ T , equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hardcore repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

An improved DNA force field for ssDNA interactions with gold nanoparticles
View Description Hide DescriptionThe widespread applications of singlestranded DNA (ssDNA) conjugated gold nanoparticles (AuNPs) have spurred an increasing interest in the interactions between ssDNA and AuNPs. Despite extensive studies using the most sophisticated experimental techniques, the detailed molecular mechanisms still remain largely unknown. Large scale molecular dynamics (MD) simulations can thus be used to supplement experiments by providing complementary information about ssDNAAuNP interactions. However, up to now, all modern force fields for DNA were developed based on the properties of doublestranded DNA (dsDNA) molecules, which have hydrophilic outer backbones “protecting” hydrophobic inner nucleobases from water. Without the doublehelix structure of dsDNA and thus the “protection” by the outer backbone, the nucleobases of ssDNA are directly exposed to solvent, and their behavior in water is very different from that of dsDNA, especially at the interface with nanoparticles. In this work, we have improved the force field of ssDNA for use with nanoparticles, such as AuNPs, based on recent experimental results and quantum mechanics calculations. With the new improved force field, we demonstrated that a poly(A) sequence adsorbed on a AuNP surface is much more stable than a poly(T) sequence, which is consistent with recent experimental observations. On the contrary, the current standard force fields, including AMBER03, CHARMM27, and OPLSAA, all gave erroneous results as compared to experiments. The current improved force field is expected to have wide applications in the study of ssDNA with nanomaterials including AuNPs, which might help promote the development of ssDNAbased biosensors and other bionanodevices.

Configuration interaction wave functions: A seniority number approach
View Description Hide DescriptionThis work deals with the configuration interaction method when an Nelectron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the senioritybased configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the Nelectron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected Nelectron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.

Maximal entropy random walk improves efficiency of trapping in dendrimers
View Description Hide DescriptionWe use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the trap, as well as an exact formula for the average trapping time (ATT), which is the average of the sourcetotrap mean first passage time over all nontrap starting nodes. Based on the obtained closedform solution for ATT, we further deduce an upper bound for the leading behavior of ATT, which is the fourth power of ln N, where N is the system size. This upper bound is much smaller than the ATT of trapping depicted by unbiased random walk in Cayley trees, the leading scaling of which is a linear function of N. These results show that MERW can substantially enhance the efficiency of trapping performed in dendrimers.

Fast and anisotropic flexibilityrigidity index for protein flexibility and fluctuation analysis
View Description Hide DescriptionProtein structural fluctuation, typically measured by DebyeWaller factors, or Bfactors, is a manifestation of protein flexibility, which strongly correlates to protein function. The flexibilityrigidity index (FRI) is a newly proposed method for the construction of atomic rigidity functions required in the theory of continuum elasticity with atomic rigidity, which is a new multiscale formalism for describing excessively large biomolecular systems. The FRI method analyzes protein rigidity and flexibility and is capable of predicting protein Bfactors without resorting to matrix diagonalization. A fundamental assumption used in the FRI is that protein structures are uniquely determined by various internal and external interactions, while the protein functions, such as stability and flexibility, are solely determined by the structure. As such, one can predict protein flexibility without resorting to the protein interaction Hamiltonian. Consequently, bypassing the matrix diagonalization, the original FRI has a computational complexity of . This work introduces a fast FRI (fFRI) algorithm for the flexibility analysis of large macromolecules. The proposed fFRI further reduces the computational complexity to . Additionally, we propose anisotropic FRI (aFRI) algorithms for the analysis of protein collective dynamics. The aFRI algorithms permit adaptive Hessian matrices, from a completely global 3N × 3N matrix to completely local 3 × 3 matrices. These 3 × 3 matrices, despite being calculated locally, also contain nonlocal correlation information. Eigenvectors obtained from the proposed aFRI algorithms are able to demonstrate collective motions. Moreover, we investigate the performance of FRI by employing four families of radial basis correlation functions. Both parameter optimized and parameterfree FRI methods are explored. Furthermore, we compare the accuracy and efficiency of FRI with some established approaches to flexibility analysis, namely, normal mode analysis and Gaussian network model (GNM). The accuracy of the FRI method is tested using four sets of proteins, three sets of relatively small, medium, and largesized structures and an extended set of 365 proteins. A fifth set of proteins is used to compare the efficiency of the FRI, fFRI, aFRI, and GNM methods. Intensive validation and comparison indicate that the FRI, particularly the fFRI, is orders of magnitude more efficient and about 10% more accurate overall than some of the most popular methods in the field. The proposed fFRI is able to predict Bfactors for αcarbons of the HIV virus capsid (313 236 residues) in less than 30 seconds on a single processor using only one core. Finally, we demonstrate the application of FRI and aFRI to protein domain analysis.

Relativistic nuclear magnetic resonance Jcoupling with ultrasoft pseudopotentials and the zerothorder regular approximation
View Description Hide DescriptionWe present a method for the firstprinciples calculation of nuclear magnetic resonance (NMR) Jcoupling in extended systems using stateoftheart ultrasoft pseudopotentials and including scalarrelativistic effects. The use of ultrasoft pseudopotentials is allowed by extending the projector augmented wave (PAW) method of Joyce et al. [J. Chem. Phys.127, 204107 (2007)]. We benchmark it against existing localorbital quantum chemical calculations and experiments for small molecules containing light elements, with good agreement. Scalarrelativistic effects are included at the zerothorder regular approximation level of theory and benchmarked against existing localorbital quantum chemical calculations and experiments for a number of small molecules containing the heavy row six elements W, Pt, Hg, Tl, and Pb, with good agreement. Finally, ^{1}J(PAg) and ^{2}J(PAgP) couplings are calculated in some larger molecular crystals and compared against solidstate NMR experiments. Some remarks are also made as to improving the numerical stability of dipole perturbations using PAW.

Eckart−Sayvetz conditions revisited
View Description Hide DescriptionIt is shown that vibrational displacements satisfying the Eckart−Sayvetz conditions can be constructed by projection of unconstrained displacements. This result has a number of interesting direct and indirect ramifications: (i) The normal coordinates corresponding to an electronic state or an isotopologue of a molecule are transformed to those of another state or isotopologue by a linear and, in general, nonorthogonal transformation. (ii) Novel interpretation of axis switching. (iii) One may enhance the separation of rotationallargeamplitude internal motions and the vibrational motions beyond that offered by the standard use of the Eckart−Sayvetz conditions. (iv) The rotationalvibrational Hamiltonian given in terms of curvilinear internal coordinates may be derived with elementary mathematical tools while taking into account the Eckart conditions with or without enhancement.

Correlation correction to configuration interaction singles from coupled cluster perturbation theory
View Description Hide DescriptionA new state specific correlation correction to configuration interaction singles (CIS) excitation energies is presented using coupled cluster perturbation theory (CCPT). General expressions for CISCCPT are derived and expanded explicitly to firstorder in the wavefunction and secondorder in the energy. By virtue of the nature of CCPT this method is a priori size extensive and incorporates infiniteorder effects into the wavefunction. This results in a balanced singles space excited state theory that at secondorder is an improvement over the ubiquitous CIS(D) method and comparable in quality to equation of motion coupled cluster (EOMCC). A modest test set composed of the first four excited states from nine small organic molecules was used to quantify the accuracy and consistency of the CISCCPT2 excitation energies and density of states. We find that CISCCPT2 has a standard deviation error of 0.18 eV for excitation energies and 0.14 eV for density of states compared to EOMCC, a factor of two better than CIS(D) with a significant reduction in the maximum deviation as well.

Modeling timecoincident ultrafast electron transfer and solvation processes at moleculesemiconductor interfaces
View Description Hide DescriptionKinetic models based on Fermi's Golden Rule are commonly employed to understand photoinduced electron transfer dynamics at moleculesemiconductor interfaces. Implicit in such secondorder perturbative descriptions is the assumption that nuclear relaxation of the photoexcited electron donor is fast compared to electron injection into the semiconductor. This approximation breaks down in systems where electron transfer transitions occur on 100fs time scale. Here, we present a fourthorder perturbative model that captures the interplay between timecoincident electron transfer and nuclear relaxation processes initiated by light absorption. The model consists of a fairly small number of parameters, which can be derived from standard spectroscopic measurements (e.g., linear absorbance, fluorescence) and/or firstprinciples electronic structure calculations. Insights provided by the model are illustrated for a twolevel donor molecule coupled to both (i) a single acceptor level and (ii) a density of states (DOS) calculated for TiO2 using a firstprinciples electronic structure theory. These numerical calculations show that secondorder kinetic theories fail to capture basic physical effects when the DOS exhibits narrow maxima near the energy of the molecular excited state. Overall, we conclude that the present fourthorder rate formula constitutes a rigorous and intuitive framework for understanding photoinduced electron transfer dynamics that occur on the 100fs time scale.

Calculation of statetostate differential and integral cross sections for atomdiatom reactions with transitionstate wave packets
View Description Hide DescriptionA recently proposed transitionstate wave packet method [R. Welsch, F. HuarteLarrañaga, and U. Manthe, J. Chem. Phys.136, 064117 (2012)] provides an efficient and intuitive framework to study reactive quantum scattering at the statetostate level. It propagates a few transitionstate wave packets, defined by the eigenfunctions of the lowrank thermal flux operator located near the transition state, into the asymptotic regions of the reactant and product arrangement channels separately using the corresponding Jacobi coordinates. The entire Smatrix can then be assembled from the corresponding fluxflux crosscorrelation functions for all arrangement channels. Since the transitionstate wave packets can be defined in a relatively small region, its transformation into either the reactant or product Jacobi coordinates is accurate and efficient. Furthermore, the grid/basis for the propagation, including the maximum helicity quantum number K, is much smaller than that required in conventional wave packet treatments of statetostate reactive scattering. This approach is implemented for atomdiatom reactions using a timedependent wave packet method and applied to the H + D2 reaction with all partial waves. Excellent agreement with benchmark integral and differential cross sections is achieved.

On energetic prerequisites of attracting electrons
View Description Hide DescriptionThe internal reorganization energy and the zeropoint vibrational energy (ZPE) of fractionally charged molecules embedded in molecular materials are discussed. The theory for isolated open quantum systems is taken as the starting point. It is shown that for isolated molecules the internal reorganizationenergy function and its slope, i.e., the chemical potential of an open molecular system are monotonically decreasing functions with respect to increasing amount of negative excess charge (q) in the range of q = [0, 1]. Calculations of the ZPE for fractionally charged molecules show that the ZPE may have a minimum for fractional occupation. The calculations show that the internal reorganization energy and changes in the ZPE are of the same order of magnitude with different behavior as a function of the excess charge. The sum of the contributions might favor molecules with fractional occupation of the molecular units and partial delocalization of the excess electrons in solidstate materials also when considering Coulomb repulsion between the excess electrons. The fractional electrons are then coherently distributed on many molecules of the solidstate material forming a condensate of attracting electrons, which is crucial for the superconducting state.

Extension and evaluation of the multilevel summation method for fast longrange electrostatics calculations
View Description Hide DescriptionSeveral extensions and improvements have been made to the multilevel summation method (MSM) of computing longrange electrostatic interactions. These include pressure calculation, an improved error estimator, faster direct part calculation, extension to nonorthogonal (triclinic) systems, and parallelization using the domain decomposition method. MSM also allows fully nonperiodic longrange electrostatics calculations which are not possible using traditional Ewaldbased methods. In spite of these significant improvements to the MSM algorithm, the particleparticle particlemesh (PPPM) method was still found to be faster for the periodic systems we tested on a single processor. However, the fast Fourier transforms (FFTs) that PPPM relies on represent a major scaling bottleneck for the method when running on many cores (because the manytomany communication pattern of the FFT becomes expensive) and MSM scales better than PPPM when using a large core count for two test problems on Sandia's Redsky machine. This FFT bottleneck can be reduced by running PPPM on only a subset of the total processors. MSM is most competitive for relatively low accuracy calculations. On Sandia's Chama machine, however, PPPM is found to scale better than MSM for all core counts that we tested. These results suggest that PPPM is usually more efficient than MSM for typical problems running on current high performance computers. However, further improvements to MSM algorithm could increase its competitiveness for calculation of longrange electrostatic interactions.

Modeling intrinsic defects in LiNbO_{3} within the SlaterJanak transition state model
View Description Hide DescriptionIntrinsic point defects in LiNbO3, i.e., isolated Nb antisites and Li as well Nb vacancies, are investigated from firstprinciples within the SlaterJanak transition state model. Thereby the electronic structure of the investigated defects is calculated with hybrid exchangecorrelation functionals. This approach allows for the calculation of charge transition levels without comparing the total energies of differently charged supercells. The obtained results are in agreement with previous hybrid densityfunctional theory calculations based on totalenergy differences. Li and Nb vacancies can be formed in the and charge states only, as long as the host is not strongly ptype or ntype, respectively. Nb Li antisites may capture one or two electrons, forming the defect states often referred to as small bound polaron and bipolaron.

Dirac cones in the spectrum of bonddecorated graphenes
View Description Hide DescriptionWe present a twoband model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of twodimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary πelectron Hückel networks into each of the three carbon–carbon πbonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting twodimensional πnetworks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.

Dynamic density functional theory with hydrodynamic interactions and fluctuations
View Description Hide DescriptionWe derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett.101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (noninteracting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamicallycorrelated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. VandenEijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

How to remove the spurious resonances from ring polymer molecular dynamics
View Description Hide DescriptionTwo of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the ParrinelloRahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the shorttime limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.
 Advanced Experimental Techniques

Measuring chirality in NMR in the presence of a timedependent electric field
View Description Hide DescriptionTraditional nuclear magnetic resonance (NMR) experiments are “blind” to chirality since the spectra for left and right handed enantiomers are identical in an achiral medium. However, theoretical arguments have suggested that the effective Hamiltonian for spin1/2 nuclei in the presence of electric and magnetic fields can be different for left and right handed enantiomers, thereby enabling NMR to be used to spectroscopically detect chirality even in an achiral medium. However, most proposals to detect the chiral NMR signature require measuring signals that are equivalent to picomolar concentrations for ^{1}H nuclei, which are outside current NMR detection limits. In this work, we propose to use an AC electric field that is resonantly modulated at the Larmor frequency, thereby enhancing the effect of the chiral term by four to six orders of magnitude. We predict that a steadystate transverse magnetization, whose direction will be opposite for different enantiomers, will build up during application of an AC electric field. We also propose an experimental setup that uses a solenoid coil with an AC current to generate the necessary periodic electric fields that can be used to generate chiral signals which are equivalent to the signal from a ^{1}H submicromolar concentration.