Efficient calculation of integrals in mixed ramp-Gaussian basis sets

Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp.These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms

Getting Past the Language Gap: Innovations in Machine Translation

In this chapter, we will be reviewing state of the art machine translation systems, and will discuss innovative methods for machine translation, highlighting the most promising techniques and applications. Machine translation (MT) has benefited from a revitalization in the last 10 years or so, after a period of relatively slow activity. In 2005 the field received a jumpstart when a powerful complete experimental package for building MT systems from scratch became freely available as a result of the unified efforts of the MOSES international consortium. Around the same time, hierarchical methods had been introduced by Chinese researchers, which allowed the introduction and use of syntactic information in translation modeling. Furthermore, the advances in the related field of computational linguistics, making off-the-shelf taggers and parsers readily available, helped give MT an additional boost. Yet there is still more progress to be made. For example, MT will be enhanced greatly when both syntax and semantics are on board: this still presents a major challenge though many advanced research groups are currently pursuing ways to meet this challenge head-on. The next generation of MT will consist of a collection of hybrid systems. It also augurs well for the mobile environment, as we look forward to more advanced and improved technologies that enable the working of Speech-To-Speech machine translation on hand-held devices, i.e. speech recognition and speech synthesis. We review all of these developments and point out in the final section some of the most promising research avenues for the future of MT

Electron-vibration entanglement in the Born-Oppenheimer description of chemical reactions and spectroscopy

This journal is © the Owner Societies. Entanglement is sometimes regarded as the quintessential measure of the quantum nature of a system and its significance for the understanding of coupled electronic and vibrational motions in molecules has been conjectured. Previously, we considered the entanglement developed in a spatially localized diabatic basis representation of the electronic states, considering design rules for qubits in a low-temperature chemical quantum computer. We extend this to consider the entanglement developed during high-energy processes. We also consider the entanglement developed using adiabatic electronic basis, providing a novel way for interpreting effects of the breakdown of the Born-Oppenheimer (BO) approximation. We consider: (i) BO entanglement in the ground-state wavefunction relevant to equilibrium thermodynamics, (ii) BO entanglement associated with low-energy wavefunctions relevant to infrared and tunneling spectroscopies, (iii) BO entanglement in high-energy eigenfunctions relevant to chemical reaction processes, and (iv) BO entanglement developed during reactive wavepacket dynamics. A two-state single-mode diabatic model descriptive of a wide range of chemical phenomena is used for this purpose. The entanglement developed by BO breakdown correlates simply with the diameter of the cusp introduced by the BO approximation, and a hierarchy appears between the various BO-breakdown correction terms, with the first-derivative correction being more important than the second-derivative correction which is more important than the diagonal correction. This simplicity is in contrast to the complexity of BO-breakdown effects on thermodynamic, spectroscopic, and kinetic properties. Further, processes poorly treated at the BO level that appear adequately treated using the Born-Huang adiabatic approximation are found to have properties that can only be described using a non-adiabatic description. For the entanglement developed between diabatic electronic states and the nuclear motion, qualitatively differently behavior is found compared to traditional properties of the density matrix and hence entanglement provides new information about system properties. For chemical reactions, this type of entanglement simply builds up as the transition-state region is crossed. It is robust to small changes in parameter values and is therefore more attractive for making quantum qubits than is the related fragile ground-state entanglement, provided that coherent motion at the transition state can be sustained

An update to the MARVEL data set and ExoMol line list for ¹²C₂

The spectrum of dicarbon (C_{2}) is important in astrophysics and for spectroscopic studies of plasmas and flames. The C_{2} spectrum is characterized by many band systems with new ones still being actively identified; astronomical observations involve eight of these bands. Recently, Furtenbacher et al. presented a set of 5699 empirical energy levels for {12}^C_{2}, distributed among 11 electronic states and 98 vibronic bands, derived from 42 experimental studies and obtained using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. Here, we add data from 13 new sources and update data from 5 sources. Many of these data sources characterize high-lying electronic states, including the newly detected 3 {3}^Π_{g} state. Older studies have been included following improvements in the MARVEL procedure that allow their uncertainties to be estimated. These older works in particular determine levels in the C {1}^Π_{g} state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C {1}^Π_{g}–A {1}^Π_{u}) band. The new compilation considers a total of 31 323 transitions and derives 7047 empirical (MARVEL) energy levels spanning 20 electronic and 142 vibronic states. These new empirical energy levels are used here to update the 8states C_{2} ExoMol line list This updated line list is highly suitable for high-resolution cross-correlation studies in astronomical spectroscopy of, for example, exoplanets, as 99.4 per cent of the transitions with intensities over 10^{−18} cm molecule^{−1} at 1000 K have frequencies determined by empirical energy levels

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of 48 Ti 16 O

Accurate, experimental rovibronic energy levels, with associated labels and uncertainties, are reported for 11 low-lying electronic states of the diatomic ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ molecule, determined using the Marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. All levels are based on lines corresponding to critically reviewed and validated high-resolution experimental spectra taken from 24 literature sources. The transition data are in the 2–22,160 cm−1 region. Out of the 49,679 measured transitions, 43,885 are triplet–triplet, 5710 are singlet–singlet, and 84 are triplet–singlet transitions. A careful analysis of the resulting experimental spectroscopic network (SN) allows 48,590 transitions to be validated. The transitions determine 93 vibrational band origins of ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$, including 71 triplet and 22 singlet ones. There are 276 (73) triplet–triplet (singlet–singlet) band-heads derived from Marvel experimental energies, 123(38) of which have never been assigned in low- or high-resolution experiments. The highest J value, where J stands for the total angular momentum, for which an energy level is validated is 163. The number of experimentally derived triplet and singlet ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ rovibrational energy levels is 8682 and 1882, respectively. The lists of validated lines and levels for ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ are deposited in the supporting information to this paper

ExoMol molecular line lists – XXVI: spectra of SH and NS

Line lists for the sulphur-containing molecules SH (the mercapto radical) and NS are computed as part of the ExoMol project. These line lists consider transitions within the X2Π ground state for 32SH, 33SH, 34SH,36SH and, 32SD, and 14N32S, 14N33S, 14N34S, 14N36S, and 15N32S. Ab initio potential energy (PEC) and spin-orbit coupling (SOC) curves are computed and then improved by fitting to experimentally observed transitions. Fully ab initio dipole moment curves (DMCs) computed at high level of theory are used to produce the final line lists. For SH, our fit gives a root-mean-square (rms) error of 0.03 cm−1 between the observed (⁠vmax = 4, Jmax = 34.5) and calculated transitions wavenumbers; this is extrapolated such that all X2Π rotational-vibrational-electronic (rovibronic) bound states are considered. For 32SH the resulting line list contains about 81 000 transitions and 2300 rovibronic states, considering levels up to vmax = 14 and Jmax = 60.5. For NS the refinement used a combination of experimentally determined frequencies and energy levels and led to an rms-fitting error of 0.002 cm−1. Each NS-calculated line list includes around 2.8 million transitions and 31 000 rovibronic states with a vibrational range up to v = 53 and rotational range up to J = 235.5, which covers up to 23 000 cm−1. Both line lists should be complete for temperatures up to 5000 K. Example spectra simulated using this line list are shown and comparisons made to the existing data in the CDMS data base. The line lists are available from the CDS (http://cdsarc.u-strasbg.fr) and ExoMol (www.exomol.com) data bases

Bringing pupils into the ORBYTS of research

Most scientists would consider themselves lucky to publish a research paper while still an undergraduate, but a group of pupils at Highams Park School in East London has co-authored a paper at age 18, thanks to ORBYTS. Original Research By Young Twinkle Scientists (ORBYTS) comprises the core part of EduTwinkle, the education and outreach arm of the upcoming exoplanet space mission Twinkle, led by UK scientists and engineers, and is aimed at A-level students. ORBYTS was founded in 2016 by Clara Sousa-Silva, who was splitting her time teaching at Highams Park School and working as a postdoc at University College London, via the Researchers in Schools programme. This blend of education and research inspired her to set up a scheme enabling young postdoc and PhD students from her research group at UCL, ExoMol, to perform novel research with some of her sixth-form students. ORBYTS now involves more than 30 pupils in eight schools across the UK

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of (ZrO)-Zr-90-O-16

Zirconium oxide (ZrO) is an important astrophysical molecule that defines the S-star classification class for cool giant stars. Accurate, empirical rovibronic energy levels, with associated labels and uncertainties, are reported for nine low-lying electronic states of the diatomic 90 16 Zr O molecule. These 8088 empirical energy levels are determined using the Measured Active Rotational-Vibrational Energy Levels algorithm with 23,317 input assigned transition frequencies, 22,549 of which were validated during this study. A temperature-dependent partition function is presented alongside updated spectroscopic constants for the nine low-lying electronic states

The ExoMol database: Molecular line lists for exoplanet and other hot atmospheres

The ExoMol database (www.exomol.com) provides extensive line lists of molecular transitions which are valid over extended temperature ranges. The status of the current release of the database is reviewed and a new data structure is specified. This structure augments the provision of energy levels (and hence transition frequencies) and Einstein A coefficients with other key properties, including lifetimes of individual states, temperature-dependent cooling functions, Landé g-factors, partition functions, cross sections, k-coefficients and transition dipoles with phase relations. Particular attention is paid to the treatment of pressure broadening parameters. The new data structure includes a definition file which provides the necessary information for utilities accessing ExoMol through its application programming interface (API). Prospects for the inclusion of new species into the database are discussed