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

Two-colour photoionization resonance spectroscopy of NO: Complete separation of rotational levels of NO+ at the ionization threshold

Recent advances in the understanding of the factors which determine line intensities in zero kinetic energy photoelectron spectroscopy (ZEKE-PES) are reviewed. The relative importance of direct ionization and autoionization is assessed. Explicit consideration of the channel interactions which take place in the vicinity of molecular ionization thresholds leads to a general discussion of rotational line intensities in ZEKE-PES. A series of limiting cases is proposed to assist in the interpretation of experimental results. Finally a new dynamical interpretation of ZEKE experiments based on the trapping of the ZEKE electrons in non-penetrating high-l Rydberg orbitals by weak electric fields appears to give a satisfactory explanation of most experimental results obtained to date.

Rotational line intensities in zero kinetic energy photoelectron spectroscopy (ZEKE-PES)

The 584 A photoelectron spectra of supersonic molecular beams of H2O and D2O have been obtained with improved resolution. The spectroscopic constants of the X 2B1 and A 2A1 state ions, including ω01, x011, ω02, x022, and x012, are reported. For the first two electronic states of the ion, precise line splittings were evaluated with a least squares fitting procedure, employing sums of empirical instrument response functions and a linear background. A simulation of the vibrational manifolds of the B 2B2 state ions with combination progressions in the symmetry‐allowed modes ν1 and ν2 failed to reproduce the diffuse photoelectron bands observed for both H2O and D2O. Autocorrelation functions were calculated from the photoelectron bands of all three electronic states. The B 2B2 state correlation functions exhibit ultrafast decay, occurring on a 10−14 s time scale. The ν2 motion appears to define the decay in the correlation function. This behavior supports a previously proposed B 2B2–A 2A1 curve‐crossing model for the nonradiative relaxation of the B 2B2 state ions.

https://escholarship.org/content/qt42k534gh/qt42k534gh.pdf?t=p0uw06

Molecular beam photoelectron spectroscopy and femtosecond intramolecular dynamics of H2O+ and D2O+

https://escholarship.org/content/qt7tw2b559/qt7tw2b559.pdf?t=p0fw5y

High resolution UV photoelectron spectroscopy of CO+2, COS+ and CS+2 using supersonic molecular beams

The 584 A photoelectron spectra of rotationally cold C2H2 and C2D2 were obtained with improved resolution, permitting the first three electronic states of the ions to be characterized in greater detail. Temperature‐dependent studies led to a definitive assignment of the low intensity features in the X 2∏u state, yielding ν4=837±12 cm−1 for C2H+2 and ν4=702±12 cm−1 for C2D+2. The ν5 origin of the Renner–Teller multiplet was identified. In the case of C2D+2, a Fermi resonance with this multiplet contributed intensity to the ν1 mode, facilitating its evaluation at 2572±16 cm−1. The C2h geometry of the A 2Ag state was determined from the two previously unobserved bending progressions, assigned to ν4 and ν5B, and evaluated at 492±12 and 605±12 cm−1 for C2H+2 and 339±12 and 516±12 cm−1 for C2D+2, respectively. A more extensive vibrational progression than previously evident, comprised of irregular spectral features indicative of nonadiabatic effects, was observed for the B 2∑+u state. Autocorrelation functions were derived from the spectra for all three electronic states, and the two electronically excited states exhibit an ultrafast decay on a 10−14 s time scale. The A 2Ag state decays within one period of bending vibration, while the B 2∑+u state survives only 14 fs, corresponding to a single period of symmetric stretching motion.

/pdf/photoelectron-spectroscopy-and-inferred-femtosecond-4suqrf6uds.pdf

Photoelectron spectroscopy and inferred femtosecond intramolecular dynamics of C2H+2 and C2D+2

The 584 A photoelectron spectra of n‐H2, p‐H2, HD, and D2 were recorded at a resolution of 11 meV FWHM using a supersonic molecular beam source. Spectra were taken at several stagnation temperatures and pressures in order to vary the rotational population distribution in the beam with a corresponding variation in the relative intensities of the rotational transitions. Many of the Q‐branch components were resolved for the first time. ΔG(v+1/2) and Bv values were measured for all observed vibrational states of H+2, HD+, and D+2 and were used to determined the ionic vibrational and rotational constants: ωe, ωexe, ωeye, ωeze, Be, and αe. The results represent a substantial improvement over previous experimental determinations and were found to be consistent with the available theoretical rotation‐vibration energy levels. The measurement of the intensity distribution of photoelectrons as a function of vibrational states yielded photoionization cross sections which were in good agreement with the theoretical va...

/pdf/rotationally-resolved-photoelectron-spectroscopy-of-n-h2-p-1ncjw308vv.pdf

Rotationally resolved photoelectron spectroscopy of n‐H2, p‐H2, HD, and D2

The 584 A photoelectron spectrum of ethylene was reexamined at higher resolution using a supersonic molecular beam source for rotational cooling. The vibrational frequencies of the C/sub 2/H/sup +//sub 4/X /sup 2/B/sub 3/ state were measured with improved accuracy, which permitted the torsional potential energy curve to be characterized. The measured equilibrium torsional angle is 27/sup 0/*2/sup 0/, and the inversion barrier is 270 +- 150 cm/sup -1/. The A /sup 2/B/sub 3/ state is shown to be in reasonable agreement with a recent theoretical calculation which takes into account strong nonadiabatic effects. The correlation function calculated for this state is consistent with this calculation and recent calculations on the unimolecular dissociation of this state. The B /sup 2/A state correlation function indicates a rapid decay mechanism is operative. The broadened vibrational structure in the fourth band results from a saddle point in the C /sup 2/B/sub 2/ potential energy surface from which the ion relaxes to the X state by moving along a repulsive degree of freedom, which in this case is internal rotation. The C state vibrational broadening as well as the decay of the correlation function yield a lifetime for this process of 7 fs.

Torsional potential and intramolecular dynamics in the C/sub 2/H/sup +//sub 4/ photoelectron spectra

The 584 A photoelectron spectra of n-H/sub 2/, p-H/sub 2/, HD, and D/sub 2/ were recorded at a resolution of 11 meV FWHM using a supersonic molecular beam source. Spectra were taken at several stagnation temperatures and pressures in order to vary the rotational population distribution in the beam with a corresponding variation in the relative intensities of the rotational transitions. Many of the Q-branch components were resolved for the first time. ..delta..G(v+1/2) and B/sub v/ values were measured for all observed vibrational states of H/sup +//sub 2/, HD/sup +/, and D/sup +//sub 2/ and were used to determined the ionic vibrational and rotational constants: ..omega../sub e/, ..omega../sub e/x/sub e/, ..omega../sub e/y/sub e/, ..omega../sub e/z/sub e/, B/sub e/, and ..cap alpha../sub e/. The results represent a substantial improvement over previous experimental determinations and were found to be consistent with the available theoretical rotation-vibration energy levels. The measurement of the intensity distribution of photoelectrons as a function of vibrational states yielded photoionization cross sections which were in good agreement with the theoretical values calculated by O'Niel and Reinhardt.

J. E. Reutt

Papers

Photoelectron spectroscopy and inferred femtosecond intramolecular dynamics of C2H+2 and C2D+2

Rotationally resolved photoelectron spectroscopy of n‐H2, p‐H2, HD, and D2

Torsional potential and intramolecular dynamics in the C/sub 2/H/sup +//sub 4/ photoelectron spectra

Rotationally resolved photoelectron spectroscopy of n-H/sub 2/, p-H/sub 2/, HD, and D/sub 2/

Photoelectron Spectroscopy and Inferred Femtosecond Intramolecular Dynamics of C2H2+and C2D2+.