measurements-long-range-electronic-correlations-during-femtosecond

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

The precise details of the interaction of intense X-ray pulses with matter are a topic of intense interest to researchers attempting to interpret the ...

University of Melbourne

An implementation of the generalized gradient approximation within the four-component formulation of relativistic density-functional theory using G-spinor basis sets is presented. This approach is based on the direct evaluation of the relativistic density and its gradient from the G-spinor amplitudes and gradients without explicit reference to the total density matrix. This proves to be a particularly efficient scheme, with an intrinsic computational cost that scales linearly with the number of G-spinor basis functions. In order to validate this new implementation, incorporated in the parallel version of the program BERTHA, a detailed study of the diatomic system CsAu is also reported. The spectroscopic constants D(e),r(e),omega(e), and x(e)omega(e) and the dipole moment mu have been calculated and compared with the best available theoretical and experimental data. The sensitivity of our results to the details of the numerical schemes used to evaluate the matrix elements is analyzed in detail. Also presented is a comparative study of molecular properties in the alkali auride series which have been obtained using several standard non-relativistic density functionals.

Computational strategies for a four-component Dirac-Kohn-Sham program: implementation and first applications.

Spectroscopic constants, including dissociation energies, harmonic and anharmonic vibrational frequencies, and dipole moments, are calculated for the complete alkali auride series (LiAu, NaAu, KAu, RbAu, CsAu). The four-component formulation of relativistic density functional theory has been employed in this study, using the G-spinor basis sets implemented recently in the program BERTHA. The performance of four standard nonrelativistic density functionals employed is investigated by comparing the results with the best available theoretical and experimental data. The present work provides the first theoretical predictions on the molecular properties of RbAu. The intermetallic bond that occurs in the alkali auride series is highly polar and is characterized by a large charge transfer from the alkali metals to gold. The extent of this electron transfer has been investigated using several different charge analysis methods, enabling us to reach some general conclusions on their relative performance. We further report a detailed analysis of the topological properties of relativistic electron density in the bonding region, discussing the features of this approach which characterize the nature of the chemical bond. We have also computed the fully relativistic density for the alkali halides MBr and MI (M = Li, Na, K, Rb, and Cs). The comparative study shows that, on the basis of several topological properties and the variation in bond lengths, the gold atom behaves similarly to a halogen intermediate between Br and I.

The electronic structure of alkali aurides. A four-component Dirac-Kohn-Sham study.

A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2, Au3+, Au4, Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+.

Electron density fitting for the Coulomb problem in relativistic density-functional theory.

The nuclear quadrupole moment for (197)Au has been determined on the base of the state-of-art relativistic molecular calculations. The experimental shifts in the nuclear coupling constants in the series of molecules AuF, XeAuF, KrAuF, ArAuF, (OC)AuF, and AuH have been combined with highly accurate determinations of the electric field gradient (EFG) at the gold nucleus, obtained by molecular relativistic Dirac-Coulomb-Gaunt Hartree-Fock calculations. The electronic correlation contribution to the EFG is included with the CCSD(T) and CCSD-T approaches, also in the four-component framework, using a finite-difference method. In order to estimate the accuracy of their approach the authors have thoroughly investigated the convergence of the results with respect to the basis set employed and the size of the correlated orbital space. The effect of the full Breit electron-electron interaction on the nuclear quadrupole moment of gold has also been considered explicitly for the AuF molecule. They obtain for (197)Au a nuclear quadrupole moment of 510+/-15 mb, which deviates by about 7% from the currently accepted muonic value.

Nuclear electric quadrupole moment of gold.

We present recent developments in the implementation of the density fitting approach for the Coulomb interaction within the four-component formulation of relativistic density functional theory [Belpassi et al., J. Chem. Phys. 124, 124104 (2006)]. In particular, we make use of the Poisson equation to generate suitable auxiliary basis sets and simplify the electron repulsion integrals [Manby and Knowles, Phys. Rev. Lett. 87, 163001 (2001)]. We propose a particularly simple and efficient method for the generation of accurate Poisson auxiliary basis sets, based on already available standard Coulomb fitting sets. Just as is found in the nonrelativistic case, we show that the number of standard auxiliary fitting functions that need to be added to the Poisson-generated functions in order to achieve a fitting accuracy equal or, in some cases, better than that of the standard procedure is remarkably small. The efficiency of the present implementation is demonstrated in a detailed study of the spectroscopic properties and energetics of several gold containing systems, including the Au dimer and the CsAu molecule. The extraction reaction of a H(2)O molecule from a Au(H(2)O)(9) (+) cluster is also calculated as an example of mixed heavy-light-atom molecular systems. The scaling behavior of the algorithm implemented is illustrated for some closed shell gold clusters up to Au(5) (+). The increased sparsity of the Coulomb matrices involved in the Poisson fitting is identified, as are potential computational applications and the use of the Poisson fitting for the relativistic exchange-correlation problem.

Poisson-transformed density fitting in relativistic four-component Dirac-Kohn-Sham theory.

A method is proposed that uses maximum entropy analysis of a Young's two-slit interference pattern for the measurement of the spectrum of a high-harmonic-generation light source. The approach is tested using experimental data, and the results are found to be consistent with those obtained directly using a grazing incidence spectrometer.

High-harmonic-generation spectrum reconstruction from Young's double-slits interference pattern using the maximum entropy method.

We present the first experimental demonstration of the astigmatic phase retrieval technique, in which the diffracted wavefield is distorted by cylindrical curvature in two orthogonal directions. A charge-one vortex, a charge-two vortex, and a simple test image are all correctly reconstructed.

Astigmatic phase retrieval: an experimental demonstration.

A method for numerically recovering the coherent modes and their occupancies from a known mutual optical intensity function is described. As an example, the technique is applied to previously published experimental data from an x-ray undulator source. The data are found to be described by three coherent modes, and the functional forms and relative occupancies of these modes are recovered.

Extracting coherent modes from partially coherent wavefields.

We review recent theoretical and computational advances in the full relativistic four-component Dirac-Kohn-Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite Gaussian functions, state-of-the-art density-fitting techniques and memory distributed parallelism. This approach has enormously extended the applicability of the DKS method, including for example large clusters of heavy atoms, and opens the way for future key developments. We examine the current limitations and future possible applications of the DKS approach, including the implementation of four-current density functionals and real-time propagation schemes. This would make possible to describe molecules in strong fields, accurately accounting for relativistic kinematic effects and spin-orbit coupling.

Recent advances and perspectives in four-component Dirac-Kohn-Sham calculations.

The recent development of X-ray free-electron laser sources has created new opportunities for the structural analysis of protein nanocrystals. The extremely small sizes of the crystals, as well as imperfections of the crystal structure, result in an interference phenomenon in the diffraction pattern. With decreasing crystallite size the structural imperfections play a role in the formation of the diffraction pattern that is comparable in importance to the size effects and should be taken into account during the data analysis and structure reconstruction processes. There now exists a need to develop new methods of protein structure determination that do not depend on the availability of good-quality crystals and that can treat proteins under conditions close to the active form. This paper demonstrates an approach that is specifically tailored to nanocrystalline samples and offers a unique crystallographic solution.

Continuous X-ray diffractive field in protein nanocrystallography.

We propose a new complete memory-distributed algorithm, which significantly improves the parallel implementation of the all-electron four-component Dirac-Kohn-Sham (DKS) module of BERTHA (J. Chem. Theory Comput. 2010, 6, 384). We devised an original procedure for mapping the DKS matrix between an efficient integral-driven distribution, guided by the structure of specific G-spinor basis sets and by density fitting algorithms, and the two-dimensional block-cyclic distribution scheme required by the ScaLAPACK library employed for the linear algebra operations. This implementation, because of the efficiency in the memory distribution, represents a leap forward in the applicability of the DKS procedure to arbitrarily large molecular systems and its porting on last-generation massively parallel systems. The performance of the code is illustrated by some test calculations on several gold clusters of increasing size. The DKS self-consistent procedure has been explicitly converged for two representative clusters, namely Au20 and Au34, for which the density of electronic states is reported and discussed. The largest gold cluster uses more than 39k basis functions and DKS matrices of the order of 23 GB.

Efficient Parallel All-Electron Four-Component Dirac-Kohn-Sham Program Using a Distributed Matrix Approach II.

During the last five years, serial femtosecond crystallography using X-ray laser pulses has been developed into a powerful technique for determining the atomic structures of protein molecules from micrometre- and sub-micrometre-sized crystals. One of the key reasons for this success is the 'self-gating' pulse effect, whereby the X-ray laser pulses do not need to outrun all radiation damage processes. Instead, X-ray-induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction were generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5-10 fs, but can succeed for pulses 50-100 fs in duration. It is shown here that a similar gating effect applies to single-molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of the average structure separately to the diffraction from statistical fluctuations of the structure due to damage ('damage noise'). The results suggest that sub-nanometre single-molecule imaging with 30-50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory presented opens up new experimental avenues to measure the impact of damage on single-particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.

Single-molecule imaging with longer X-ray laser pulses.

We show that all-electron relativistic four-component Dirac-Kohn-Sham (DKS) computations, using G-spinor basis sets and state-of-the-art density fitting algorithms, can be efficiently parallelized and applied to large molecular systems, including large clusters of heavy atoms. The performance of the parallel implementation of the DKS module of the program BERTHA is illustrated and analyzed by some test calculations on several gold clusters up to Au32, showing that calculations with more than 25 000 basis functions (i.e., DKS matrices on the order of 10 GB) are now feasible. As a first application of this novel implementation, we investigate the interaction of the atom Hg with the Au20 cluster.

An Efficient Parallel All-Electron Four-Component Dirac-Kohn-Sham Program Using a Distributed Matrix Approach.

Serial femtosecond X-ray crystallography (SFX) has created new opportunities in the field of structural analysis of protein nanocrystals. The intensity and timescale characteristics of the X-ray free-electron laser sources used in SFX experiments necessitate the analysis of a large collection of individual crystals of variable shape and quality to ultimately solve a single, average crystal structure. Ensembles of crystals are commonly encountered in powder diffraction, but serial crystallography is different because each crystal is measured individually and can be oriented via indexing and merged into a three-dimensional data set, as is done for conventional crystallography data. In this way, serial femtosecond crystallography data lie in between conventional crystallography data and powder diffraction data, sharing features of both. The extremely small sizes of nanocrystals, as well as the possible imperfections of their crystallite structure, significantly affect the diffraction pattern and raise the question of how best to extract accurate structure-factor moduli from serial crystallography data. Here it is demonstrated that whole-pattern fitting techniques established for one-dimensional powder diffraction analysis can be feasibly extended to higher dimensions for the analysis of merged SFX diffraction data. It is shown that for very small crystals, whole-pattern fitting methods are more accurate than Monte Carlo integration methods that are currently used.

Whole-pattern fitting technique in serial femtosecond nanocrystallography.

X-ray free-electron lasers (XFELs) deliver x-ray pulses with a coherent flux that is approximately eight orders of magnitude greater than that available from a modern third-generation synchrotron source. The power density of an XFEL pulse may be so high that it can modify the electronic properties of a sample on a femtosecond time scale. Exploration of the interaction of intense coherent x-ray pulses and matter is both of intrinsic scientific interest and of critical importance to the interpretation of experiments that probe the structures of materials using high-brightness femtosecond XFEL pulses. We report observations of the diffraction of extremely intense 32-fs nanofocused x-ray pulses by a powder sample of crystalline C60. We find that the diffraction pattern at the highest available incident power significantly differs from the one obtained using either third-generation synchrotron sources or XFEL sources operating at low output power and does not correspond to the diffraction pattern expected from any known phase of crystalline C60. We interpret these data as evidence of a long-range, coherent dynamic electronic distortion that is driven by the interaction of the periodic array of C60 molecular targets with intense x-ray pulses of femtosecond duration.

X-ray laser-induced electron dynamics observed by femtosecond diffraction from nanocrystals of Buckminsterfullerene.

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

Article	Year
Computational strategies for a four-component Dirac-Kohn-Sham program: implementation and first applications. The Journal of chemical physics\| PubMed ID: 15918696	2005
The electronic structure of alkali aurides. A four-component Dirac-Kohn-Sham study. The journal of physical chemistry. A\| PubMed ID: 16571062	2006
Electron density fitting for the Coulomb problem in relativistic density-functional theory. The Journal of chemical physics\| PubMed ID: 16599659	2006
Nuclear electric quadrupole moment of gold. The Journal of chemical physics\| PubMed ID: 17313222	2007
Poisson-transformed density fitting in relativistic four-component Dirac-Kohn-Sham theory. The Journal of chemical physics\| PubMed ID: 18376909	2008
High-harmonic-generation spectrum reconstruction from Young's double-slits interference pattern using the maximum entropy method. Optics letters\| PubMed ID: 18923616	2008
Astigmatic phase retrieval: an experimental demonstration. Optics express\| PubMed ID: 19582105	2009
Extracting coherent modes from partially coherent wavefields. Optics letters\| PubMed ID: 19823547	2009
Recent advances and perspectives in four-component Dirac-Kohn-Sham calculations. Physical chemistry chemical physics : PCCP\| PubMed ID: 21670843	2011
Continuous X-ray diffractive field in protein nanocrystallography. Acta crystallographica. Section A, Foundations of crystallography\| PubMed ID: 23250067	2013
Efficient Parallel All-Electron Four-Component Dirac-Kohn-Sham Program Using a Distributed Matrix Approach II. Journal of chemical theory and computation\| PubMed ID: 26592273	2013
Single-molecule imaging with longer X-ray laser pulses. IUCrJ\| PubMed ID: 26594374	2015
An Efficient Parallel All-Electron Four-Component Dirac-Kohn-Sham Program Using a Distributed Matrix Approach. Journal of chemical theory and computation\| PubMed ID: 26617297	2010
Whole-pattern fitting technique in serial femtosecond nanocrystallography. IUCrJ\| PubMed ID: 27006776	2016
X-ray laser-induced electron dynamics observed by femtosecond diffraction from nanocrystals of Buckminsterfullerene. Science advances\| PubMed ID: 27626076	2016
On noise-resolution uncertainty in quantum field theory. Scientific reports\| PubMed ID: 28674453	2017

Harry M. Quiney

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