One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/205/pdf

Applications of B-splines in atomic and molecular physics

Resonant X-ray Raman scattering

Visualizing chemical reactions as they occur requires atomic spatial and femtosecond temporal resolution. Here, we report imaging of the molecular structure of acetylene (C 2 H 2 ) 9 femtoseconds after ionization. Using mid-infrared laser–induced electron diffraction (LIED), we obtained snapshots as a proton departs the [C 2 H 2 ] 2+ ion. By introducing an additional laser field, we also demonstrate control over the ultrafast dissociation process and resolve different bond dynamics for molecules oriented parallel versus perpendicular to the LIED field. These measurements are in excellent agreement with a quantum chemical description of field-dressed molecular dynamics.

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Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene

Recent advances in X-ray sources have led to a renaissance in spectroscopic techniques in the X-ray region. These techniques that involve the excitation of core electrons can provide an atom specific probe of electronic structure and provide powerful analytical tools that are used in many fields of research. Theoretical calculations can often play an important role in the analysis and interpretation of experimental spectra. In this perspective, we review recent developments in quantum chemical calculations of X-ray absorption spectra, focusing on the use of time-dependent density functional theory to study core excitations. The practical application of these calculations is illustrated with examples drawn from surface science and bioinorganic chemistry, and the application of these methods to study X-ray emission spectroscopy is explored.

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Time-dependent density functional theory calculations of the spectroscopy of core electrons

The first time-resolved x-ray/optical pump-probe experiments at the SLAC Linac Coherent Light Source (LCLS) used a combination of feedback methods and post-analysis binning techniques to synchronize an ultrafast optical laser to the linac-based x-ray laser. Transient molecular nitrogen alignment revival features were resolved in time-dependent x-ray-induced fragmentation spectra. These alignment features were used to find the temporal overlap of the pump and probe pulses. The strong-field dissociation of x-ray generated quasi-bound molecular dications was used to establish the residual timing jitter. This analysis shows that the relative arrival time of the Ti:Sapphire laser and the x-ray pulses had a distribution with a standard deviation of approximately 120 fs. The largest contribution to the jitter noise spectrum was the locking of the laser oscillator to the reference RF of the accelerator, which suggests that simple technical improvements could reduce the jitter to better than 50 fs.

/pdf/time-resolved-pump-probe-experiments-at-the-lcls-3k38vpn9nb.pdf

Time-Resolved Pump-Probe Experiments at the LCLS

The angle-resolved N 1s photoelectron spectrum of has been measured with high resolution in the threshold region An analysis of the vibrational fine structure yields a vibrational energy of and a lifetime broadening of for the core-ionized molecule As in the case of C 1s ionization of CO, the vibrational fine structure changes considerably with photon energy in the region of both the shape resonance and the double excitations Both the vibrationally resolved partial photoionization cross sections and asymmetry parameters have been determined in this photon energy range The calculated cross sections in the literature are in reasonable agreement with experiment In addition, we have measured the cross sections and asymmetry parameters of the most intense direct and conjugate shake-up satellites The behaviour of the satellites is found to differ significantly from that of the corresponding C 1s satellites of CO

A high-resolution N 1s photoionization study of the molecule in the near-threshold region

Relaxation effects in C1s photoionisation of CO: a high resolution photoelectron study in the near-threshold region

The C and O $1s$ photoelectron lines of the C${\mathrm{O}}_{2}$ molecule in the gas phase have been measured with vibrational resolution in the threshold region. The vibrational fine structure on the O $1s$ line is completely dominated by the antisymmetric stretching mode with a frequency of 307 $(\ifmmode\pm\else\textpm\fi{}3)\mathrm{meV}$. This mode can be excited only via vibronic coupling, as predicted by Domcke and Cederbaum [Chem. Phys. 25, 189 (1977)], and provides a mechanism for dynamic core-hole localization. Relaxation effects are found to affect strongly the vibrational intensity distribution of the photoelectron line.

Vibrationally Resolved O 1 s Photoelectron Spectrum of CO 2 : Vibronic Coupling and Dynamic Core-Hole Localization

The C 1s photoelectron spectrum of CO has been measured with high resolution in the threshold region. The data exhibit hitherto unresolved vibrational structure on the C 1s main photoelectron line as well as new features in the satellite region. The vibrational energy of the CO + ion is 301±3 meV. The vibrational structure changes dramatically with photon energy due to the influence of the σ * shape resonance. The new satellite lines which are not present at high photon energies are attributed to conjugate shakeup processes

Photon energy dependence of the high resolution C 1s photoelectron spectrum of CO in the threshold region.

The absolute photoabsorption cross section of benzene (C6H6), encompassing the C 1s−1 π*e2u resonance, the C 1s threshold, the satellite thresholds, and extending up to 800 eV, has been measured using synchrotron radiation. Measurements of the discrete absorption structure from below the C 1s ionization threshold have been performed at high resolution. In order to unambiguously assign all structure present in the photoabsorption cross section, C 1s photoelectron spectra were measured from the C 1s threshold region up to 350 eV along with satellite spectra. The C 1s−1 single-hole and the satellite cross sections have been derived in absolute units, and their angular distributions have been determined. Resonant and normal Auger spectra were taken on the main features of the photoabsorption and single-hole cross sections. From the best resolved photoelectron spectra the underlying structure in the asymmetric benzene photoelectron peak can be partly disentangled. The experimental data show that at least two vibrational modes play a role in the C 1s photoelectron spectrum. The behavior of the investigated shake-up structure closely resembles that of ethene and ethyne, where the satellite bands due to π→π* excitations gain intensity towards threshold, an observation which may be attributed to conjugate shake-up processes. These processes lead to a significant contribution of the satellite intensity to the production of the absorption features traditionally assigned to the carbon shape resonances in benzene. An EXAFS analysis of the wide range oscillations present on the photoabsorption cross section has been performed, and reveals the C–C nearest-neighbor distance.

H. M. Köppe

Papers

A high-resolution N 1s photoionization study of the molecule in the near-threshold region

Relaxation effects in C1s photoionisation of CO: a high resolution photoelectron study in the near-threshold region

Vibrationally Resolved O 1 s Photoelectron Spectrum of CO 2 : Vibronic Coupling and Dynamic Core-Hole Localization

Photon energy dependence of the high resolution C 1s photoelectron spectrum of CO in the threshold region.

A Comprehensive Photoabsorption, Photoionization, and Shake-up Excitation Study of the C 1s Cross Section of Benzene