17 research outputs found
Hybrid variation-perturbation method for calculating rovibrational energy levels of polyatomic molecules
A procedure for calculation of rotation-vibration states of medium sized
molecules is presented. It combines the advantages of variational calculations
and perturbation theory. The vibrational problem is solved by diagonalizing a
Hamiltonian matrix, which is partitioned into two sub-blocks. The first,
smaller sub-block includes matrix elements with the largest contribution to the
energy levels targeted in the calculations. The second, larger sub-block
comprises those basis states which have little effect on these energy levels.
Numerical perturbation theory, implemented as a Jacobi rotation, is used to
compute the contributions from the matrix elements of the second sub-block.
Only the first sub-block needs to be stored in memory and diagonalized.
Calculations of the vibrational-rotational energy levels also employ a
partitioning of the Hamiltonian matrix into sub-blocks, each of which
corresponds either to a single vibrational state or a set of resonating
vibrational states, with all associated rotational levels. Physically, this
partitioning is efficient when the Coriolis coupling between different
vibrational states is small. Numerical perturbation theory is used to include
the cross-contributions from different vibrational states. Separate individual
sub-blocks are then diagonalized, replacing the diagonalization of a large
Hamiltonian matrix with a number of small matrix diagonalizations. Numerical
examples show that the proposed hybrid variational-perturbation method greatly
speeds up the variational procedure without significant loss of precision for
both vibrational-rotational energy levels and transition intensities. The
hybrid scheme can be used for accurate nuclear motion calculations on molecules
with up to 15 atoms on currently available computers.Comment: Molecular Physics (Handy Special Issue), in pres
The water vapour continuum in near-infrared windows – current understanding and prospects for its inclusion in spectroscopic databases
Spectroscopic catalogues, such as GEISA and HITRAN, do not yet include information on the water vapour continuum that pervades visible, infrared and microwave spectral regions. This is partly because, in some spectral regions, there are rather few laboratory measurements in conditions close to those in the Earth’s atmosphere; hence understanding of the characteristics of the continuum absorption is still emerging. This is particularly so in the near-infrared and visible, where there has been renewed interest and activity in recent years. In this paper we present a critical review focusing on recent laboratory measurements in two near-infrared window regions (centred on 4700 and 6300 cm−1) and include reference to the window centred on 2600 cm−1 where more measurements have been reported. The rather few available measurements, have used Fourier transform spectroscopy (FTS), cavity ring down spectroscopy, optical-feedback – cavity enhanced laser spectroscopy and, in very narrow regions, calorimetric interferometry. These systems have different advantages and disadvantages. Fourier Transform Spectroscopy can measure the continuum across both these and neighbouring windows; by contrast, the cavity laser techniques are limited to fewer wavenumbers, but have a much higher inherent sensitivity. The available results present a diverse view of the characteristics of continuum absorption, with differences in continuum strength exceeding a factor of 10 in the cores of these windows. In individual windows, the temperature dependence of the water vapour self-continuum differs significantly in the few sets of measurements that allow an analysis. The available data also indicate that the temperature dependence differs significantly between different near-infrared windows. These pioneering measurements provide an impetus for further measurements. Improvements and/or extensions in existing techniques would aid progress to a full characterisation of the continuum – as an example, we report pilot measurements of the water vapour self-continuum using a supercontinuum laser source coupled to an FTS. Such improvements, as well as additional measurements and analyses in other laboratories, would enable the inclusion of the water vapour continuum in future spectroscopic databases, and therefore allow for a more reliable forward modelling of the radiative properties of the atmosphere. It would also allow a more confident assessment of different theoretical descriptions of the underlying cause or causes of continuum absorption