Andrey Yachmenev

A Variationally Computed T = 300 K Line List for NH3†

Calculations are reported on the rotation-vibration energy levels of ammonia with associated transition intensities. A potential energy surface obtained from coupled cluster CCSD(T) calculations and subsequent fitting against experimental data is further refined by a slight adjustment of the equilibrium geometry, which leads to a significant improvement in the rotational energy level structure. A new accurate ab initio dipole moment surface is determined at the frozen core CCSD(T)/aug-cc-pVQZ level. The calculation of an extensive ammonia line list necessitates a number of algorithmic improvements in the program TROVE that is used for the variational treatment of nuclear motion. Rotation-vibration transitions for (14)NH(3) involving states with energies up to 12,000 cm(-1) and rotational quantum number J = 20 are calculated. This gives 3.25 million transitions between 184,400 energy levels. Comparisons show good agreement with data in the HITRAN database but suggest that HITRAN is missing significant ammonia absorptions, particularly in the near-infrared.

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, Lande 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.

Automatic differentiation method for numerical construction of the rotational-vibrational Hamiltonian as a power series in the curvilinear internal coordinates using the Eckart frame

We present a new numerical method to construct a rotational-vibrational Hamiltonian of a general polyatomic molecule in the Eckart frame as a power series expansion in terms of curvilinear internal coordinates. The expansion of the kinetic energy operator of an arbitrary order is obtained numerically using an automatic differentiation (AD) technique. The method is applicable to molecules of arbitrary size and structure and is flexible for choosing various types of internal coordinates. A new way of solving the Eckart-frame equations for curvilinear coordinates also based on the AD technique is presented. The resulting accuracy of the high-order expansion coefficients for the kinetic energy operator using our numerical technique is comparable to that obtained by symbolic differentiation, with the advantage of being faster and less demanding in memory. Examples for H2CO, NH3, PH3, and CH3Cl molecules demonstrate the advantages of the curvilinear internal coordinates and the Eckart molecular frame for accurate ro-vibrational calculations. Our results show that very high accuracy and quick convergence can be achieved even with moderate expansions if curvilinear coordinates are employed, which is important for applications involving large polyatomic molecules.

ExoMol line lists – VIII. A variationally computed line list for hot formaldehyde

Acomputedlinelistforformaldehyde,H2 12 C 16 O,applicabletotemperaturesuptoT =1500K is presented. An empirical potential energy and ab initio dipole moment surfaces are used as the input to the nuclear motion program TROVE. The resulting line list, referred to as AYTY, contains 10.3 million rotational-vibrational states and around 10 billion transition frequencies. Each transition includes associated Einstein-Acoefficients and absolute transition intensities,forwavenumbersbelow10000cm −1 androtationalexcitationsuptoJ =70.Roomtemperature spectra are compared with laboratory measurements and data currently available in the HITRAN data base. These spectra show excellent agreement with experimental spectra and highlight the gaps and limitations of the HITRAN data. The full line list is available from the CDS data base as well as at www.exomol.com.

Thermal averaging of the indirect nuclear spin-spin coupling constants of ammonia: The importance of the large amplitude inversion mode

Analytic internal-coordinate representations are reported for two accurate ab initio spin-spin coupling surfaces of the ammonia molecule, (1)J ((15)N,H) and (2)J(H,H). Calculations were carried out at the level of the second-order polarization propagator approximation involving coupled-cluster singles and doubles amplitudes (CCSD) and using a large specialized basis set, for a total of 841 different geometries corresponding to 2523 distinct points on the (1)J ((15)N,H) and (2)J(H,H) surfaces. The results were fitted to power series expansions truncated after the fourth-order terms. While the one-bond nitrogen-hydrogen coupling depends more on the internuclear distance, the geminal hydrogen-hydrogen coupling exhibits a pronounced dependence on the bond angle. The spin-spin parameters are first vibrationally averaged, using vibrational wave functions obtained variationally from the TROVE computer program with a CCSD(T) based potential energy surface, for ammonia and its various deuterated isotopologues. The vibrationally averaged quantities are then thermally averaged to give values of the couplings at absolute temperatures of 300 and 600 K. We find that the nuclear-motion corrections are rather small. The computed one-bond couplings and their minute isotope effects are in excellent agreement with the experimental values.

Accurate ab initio vibrational energies of methyl chloride

Two new nine-dimensional potential energy surfaces (PESs) have been generated using high-level ab initio theory for the two main isotopologues of methyl chloride, CH3 (35)Cl and CH3 (37)Cl. The respective PESs, CBS-35( HL), and CBS-37( HL), are based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set (CBS) limit, and incorporate a range of higher-level (HL) additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, scalar relativistic effects, and diagonal Born-Oppenheimer corrections. Variational calculations of the vibrational energy levels were performed using the computer program TROVE, whose functionality has been extended to handle molecules of the form XY 3Z. Fully converged energies were obtained by means of a complete vibrational basis set extrapolation. The CBS-35( HL) and CBS-37( HL) PESs reproduce the fundamental term values with root-mean-square errors of 0.75 and 1.00 cm(-1), respectively. An analysis of the combined effect of the HL corrections and CBS extrapolation on the vibrational wavenumbers indicates that both are needed to compute accurate theoretical results for methyl chloride. We believe that it would be extremely challenging to go beyond the accuracy currently achieved for CH3Cl without empirical refinement of the respective PESs.

Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

We present a general, numerically motivated approach to the construction of symmetry-adapted basis functions for solving ro-vibrational Schrödinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and, hence, to reflect the symmetry of the system. The symmetry-adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are reconstructed by solving overdetermined systems of linear equations related to the transformation properties of the corresponding wave functions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to many problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

A global potential energy surface and dipole moment surface for silane

A new nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) for silane have been generated using high-level ab initio theory. The PES, CBS-F12(HL), reproduces all four fundamental term values for (28)SiH4 with sub-wavenumber accuracy, resulting in an overall root-mean-square error of 0.63 cm(-1). The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit, and incorporates a range of higher-level additive energy corrections to account for core-valence electron correlation, higher-order coupled cluster terms, and scalar relativistic effects. Systematic errors in computed intra-band rotational energy levels are reduced by empirically refining the equilibrium geometry. The resultant Si-H bond length is in excellent agreement with previous experimental and theoretical values. Vibrational transition moments, absolute line intensities of the ν3 band, and the infrared spectrum for (28)SiH4 including states up to J = 20 and vibrational band origins up to 5000 cm(-1) are calculated and compared with available experimental results. The DMS tends to marginally overestimate the strength of line intensities. Despite this, band shape and structure across the spectrum are well reproduced and show good agreement with experiment. We thus recommend the PES and DMS for future use.

A highly accurate ab initio potential energy surface for methane.

A new nine-dimensional potential energy surface (PES) for methane has been generated using state-of-the-art ab initio theory. The PES is based on explicitly correlated coupled cluster calculations with extrapolation to the complete basis set limit and incorporates a range of higher-level additive energy corrections. These include core-valence electron correlation, higher-order coupled cluster terms beyond perturbative triples, scalar relativistic effects, and the diagonal Born-Oppenheimer correction. Sub-wavenumber accuracy is achieved for the majority of experimentally known vibrational energy levels with the four fundamentals of (12)CH4 reproduced with a root-mean-square error of 0.70 cm(-1). The computed ab initio equilibrium C-H bond length is in excellent agreement with previous values despite pure rotational energies displaying minor systematic errors as J (rotational excitation) increases. It is shown that these errors can be significantly reduced by adjusting the equilibrium geometry. The PES represents the most accurate ab initio surface to date and will serve as a good starting point for empirical refinement.

Theoretical rotation-vibration spectrum of thioformaldehyde.

We present a variational calculation of the first comprehensive T = 300 K rovibrational line list for thioformaldehyde, H2CS. It covers 41,809 rovibrational levels for states up to J(max) = 30 with vibrational band origins up to 5000 cm(-1) and provides the energies and line intensities for 547,926 transitions from the ground vibrational state to these levels. It is based on our previously reported accurate ab initio potential energy surface and a newly calculated ab initio dipole moment surface. Minor empirical adjustments are made to the ab initio equilibrium geometry to reduce systematic errors in the predicted intra-band rotational energy levels. The rovibrational energy levels and transition intensities are computed variationally by using the methods implemented in the computer program TROVE. Transition wavelengths and intensities are found to be in excellent agreement with the available experimental data. The present calculations correctly reproduce the observed resonance effects, such as intensity borrowing, thus reflecting the high accuracy of the underlying ab initio surfaces. We report a detailed analysis of several vibrational bands, especially those complicated by strong Coriolis coupling, to facilitate future laboratory assignments.