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.

In this work a new direct (noniterative) algorithm to solve the time-dependent density-functional theory equations for molecular photoionization has been proposed and implemented, using a multicentric basis set expansion of B-spline functions and complete exploiting of the molecular point-group symmetry. The method has been applied to study the photoionization dynamics of CS2 and C6H6: the results confirmed the expectation of large screening effects in CS2. For C6H6 the screening effects have been found to play a minor role than in CS2, however, also in this case the quality of the final results is definitely improved. The method has proven suitable to study with confidence molecules of medium size, and there is still room for further improvement working on more elaborate treatment of the exchange-correlation functional.

The valence shell electronic states of pyrimidine and pyrazine have been studied experimentally and theoretically. The absolute photoabsorption cross sections have been measured between 4 and 40 eV, using synchrotron radiation, and are dominated by prominent bands associated with intravalence transitions. In contrast, the structure due to Rydberg excitations is weak, but series have been observed converging onto the X 2 B 2 or D 2 B 1 limits in pyrimidine and the X 2 A g or D 2 B 3g limits in pyrazine. A comparison between the photoabsorption spectrum of pyrazine-h 4 and that for pyrazine-d 4 , together with calculated transition energies, has helped clarify the assignments of the 6a g →npb 1u and npb 2u Rydberg series. The vibrational progressions associated with these states have been assigned through analogy with those in the corresponding photoelectron band. The time-dependent version of density functional theory has been used to calculate oscillator strengths and excitation energies for the optically allowed singlet-singlet valence transitions, and also to obtain the excitation energies for electric-dipole-forbidden and/or spin-forbidden transitions. These theoretical results have allowed many of the experimentally observed bands to be assigned and provide a generally satisfactory description of the valence shell photoabsorption spectrum. Several of the prominent bands appearing above the ionization threshold can be correlated with predicted intense intravalence transitions.

The dynamical behavior of circular dichroism for valence photoionization processes in pure enantiomers of randomly oriented methyl-oxirane molecules has been studied by circularly polarized synchrotron radiation. Experimental results of the dichroism coefficient obtained for valence photoionization processes as a function of photon energy have been compared with theoretical values predicted by state-of-the-art ab initio density-functional theory. The circular dichroism measured at low electron kinetic energies was as large as 11%. Trends in the experimental dynamical behavior of the dichroism coefficients D(i)(omega) have been observed. Agreement between experimental and theoretical results permits unambiguous identification of the enantiomer and of the individual orbitals.

In the present work the photoelectron circular dichroism of camphor has been theoretically studied using B-spline and continuum multiple scattering-Xalpha methods, and comparisons are made with available experimental data. In general, rather large dichroism effects have been found for both valence and core (O 1s, C 1s) photoionizations. The agreement between the two calculations reported here and previous experimental measurements for core C 1s data is essentially quantitative. For valence ionization satisfactory agreement between theory and experiment has been obtained and the discrepancies have been attributed to both exchange-correlation potential limitations and the absence of response effects in the adopted formalism. The calculations predict, moreover, important features in the cross-section profiles, which have been discussed in terms of dipole-prepared continuum orbitals.

The linear combination of atomic orbitals B-spline density functional method has been successfully applied to a series of four chiral derivatives of oxirane, to calculate the photoionization dynamical parameters, the circular dichroism in the angular distribution effect, and to identify trends along the series. The computational algorithm has proven numerically stable and computationally competitive. The photoionization cross section, asymmetry, and dichroic parameter profiles relative to valence orbitals have been systematically studied for the states which retain their nature along the series: the identified trends have been ascribed to the different electronic properties of the substituents. A rather unexpected sensitivity of the dichroic parameter to changes in the electronic structure has been found in many instances, making this dynamical property suitable to investigate the electronic structure of chiral compounds. The magnitude of the circular dichroism in the angular distribution effect does not seem to be associated with the initial state chirality, but rather to be governed by the ability of the delocalized photoelectron wave function to probe the asymmetry of the molecular effective potential.

We report a joint experimental and theoretical study of circular dichroism in the valence photoelectron spectra of a free chiral molecule. The circular dichroism in photoelectron spectroscopy is measured at the magic angle for various valence states of Rs+d and Ss?d methyl-oxirane enantiomers in the vapor phase. The maximum dichroism measured is about 5310?2. Experimental and theoretical results are in agreement. The ab initio calculation employs a multicentric basis set of B-spline functions and a Kohn-Sham Hamiltonian

Here we present a fully ab initio study of the high-order harmonic generation (HHG) spectrum of aligned CO molecules. The calculations have been performed by using the molecular time-dependent (TD) B-spline algebraic diagrammatic construction (ADC) method. We quantitatively study how the sub-cycle laser-driven multi-channel dynamics, as reflected in the position of the dynamical minimum in the HHG spectrum, is affected by the full inclusion of both correlation-driven and laser-driven dipole interchannel couplings. We calculate channel-resolved spectral intensities as well as the phase differences between contributions of the different ionization-recombination channels to the total HHG spectrum. Our results show that electron correlation effectively controls the relative contributions of the different channels to the total HHG spectrum, leading to the opening of the new ones (1Π, 1Σ), previously disregarded for the aligned molecular setup. We conclude that inclusion of many-electron effects into the theoretical interpretation of molecular HHG spectra is essential in order to correctly extract ultrafast electron dynamics using HHG spectroscopy.