Rovibronic spectra of molecules dressed by light fields

The theory of rovibronic spectroscopy of light-dressed molecules is presented within the framework of quantum mechanically treated molecules interacting with classical light fields. Numerical applications are demonstrated for the homonuclear diatomic molecule Na$_2$, for which the general formulae can be simplified considerably and the physical processes leading to the light-dressed spectra can be understood straightforwardly. The physical origin of different peaks in the light-dressed spectrum of Na$_2$ is given and the light-dressed spectrum is investigated in terms of its dependence on the dressing field's intensity and wavelength, the turn-on time of the dressing field, and the temperature. The important implications of light-dressed spectroscopy on deriving field-free spectroscopic quantities are also discussed

MATHEMATICAL METHODS IN WATER QUALITY CONTROL

In this paper we intend to summarize the most important mathematical statistical methods which play a basic role in water quality control. In the first section we will use a random variable model and it will be shown how to observe the changing of water quality by testing homogeneity. In the second section we will compare the means of the random variables. A few new idea will be introduced in the third and fourth sections based on stochastic process models

Higher-order relativistic corrections to the vibration–rotation levels of H2S

Relativistic corrections beyond the simple one-electron mass–velocity–Darwin (MVD1) approximation to the ground-state electronic energy of H2S are determined at over 250 geometries. The corrections considered include the two-electron Darwin, the Gaunt and Breit corrections, and the one-electron Lamb shift. Fitted correction surfaces are constructed and used with an accurate ab initio nonrelativistic Born–Oppenheimer potential, determined previously (J. Chem. Phys. 115 (2001) 1229), to calculate vibrational and rotational levels for H232S. The calculations suggest that one- and two-electron relativistic corrections have a noticable influence on the levels of H2S. As for water, the effects considered have markedly different characteristics for the stretching and bending states

Analysis of measured high-resolution doublet rovibronic spectra and related line lists of 12CH and 16OH

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a multitude of modelling efforts within multiple chemical, combustion, astrophysical, and atmospheric environments. Accurate empirical rovibronic energy levels, with associated uncertainties, are reported for the low-lying doublet electronic states of 12CH and 16OH, using the Measured Active Rotational-Vibrational Energy Levels (Marvel) algorithm. For 12CH, a total of 1521 empirical energy levels are determined in the primary spectroscopic network (SN) of the radical, corresponding to the following seven electronic states: X 2Π, A 2Δ, B 2Σ−, C2 Σ+, D 2Π, E 2Σ+, and F 2Σ+. The energy levels are derived from 6348 experimentally measured and validated transitions, collected from 29 sources. For 16OH, the lowest four doublet electronic states, X 2Π, A 2Σ+, B 2Σ+, and C 2Σ+, are considered, and a careful analysis and validation of 15 938 rovibronic transitions, collected from 45 sources, results in 1624 empirical rovibronic energy levels. The large set of spectroscopic data presented should facilitate the refinement of line lists for the 12CH and 16OH radicals. For both molecules hyperfine-resolved experimental transitions have also been considered, forming SNs independent from the primary SNs

Two-electron relativistic corrections to the potential energy surface, and vibration-rotation levels of water

Two-electron relativistic corrections to the ground-state electronic energy of water are determined as a function of geometry at over 300 points. The corrections include the two-electron Darwin term (D2) of the Coulomb–Pauli Hamiltonian, obtained at the cc-pVQZ CCSD(T) level of theory, as well as the Gaunt and Breit corrections, calculated perturbationally using four-component fully variational Dirac–Hartree–Fock (DHF) wavefunctions and two different basis sets. Based on the calculated energy points, fitted relativistic correction surfaces are constructed. These surfaces are used with a high-accuracy ab initio nonrelativistic Born–Oppenheimer (BO) potential energy hypersurface to calculate vibrational band origins and rotational term values for H216O. The calculations suggest that these two-electron relativistic corrections, which go beyond the usual kinetic relativistic effects and which have so far been neglected in rovibrational calculations on light many-electron molecular systems, have a substantial influence on the rotation–vibration levels of water. The three effects considered have markedly different characteristics for the stretching and bending levels, which often leads to fortuitous cancellation of errors. The effect of the Breit interaction on the rovibrational levels is intermediate between the effect of the kinetic relativistic correction and that of the one-electron Lamb-shift effect

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 high-resolution rovibrational spectra of ¹³C¹⁶O₂

A set of empirical rovibrational energy levels, obtained through the MARVEL (measured active rotational-vibrational energy levels) procedure, is presented for the 13C16O2 isotopologue of carbon dioxide. This procedure begins with the collection and analysis of experimental rovibrational transitions from the literature, allowing for a comprehensive review of the literature on the high-resolution spectroscopy of 13C16O2, which is also presented. A total of 60 sources out of more than 750 checked provided 14,101 uniquely measured and assigned rovibrational transitions in the wavenumber range of 579–13,735 cm-1. This is followed by a weighted leastsquares refinement yielding the energy levels of the states involved in the measured transitions. Altogether 6318 empirical rovibrational energies have been determined for 13C16O2. Finally, estimates have been given for the uncertainties of the empirical energies, based on the experimental uncertainties of the transitions. The detailed analysis of the lines and the spectroscopic network built from them, as well as the uncertainty estimates, all serve to pinpoint possible errors in the experimental data, such as typos, misassignment of quantum numbers, and misidentifications. Errors found in the literature data were corrected before including them in the final MARVEL dataset and analysi

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3x10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e)(BO)=0.957 82 A and theta(e)(BO)=104.48(5)degrees, respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of (H2O)-O-16 is r(e)(ad)=0.957 85 A and theta(e)(ad)=104.50(0)degrees, respectively, while those of (D2O)-O-16 are r(e)(ad)=0.957 83 A and theta(e)(ad)=104.49(0)degrees. Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A(0) and B-0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of (H2O)-O-16, obtained from experimentally determined A(0)(') and B-0(') rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e)(sp)=0.957 77 A and theta(e)(sp)=104.48 degrees