G. Dhont

Ab initio calculation of the NH(3sigma-)-NH(3sigma-) interaction potentials in the quintet, triplet, and singlet states.

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.

Ro-vibrational excitation of the SO molecule by collision with the He atom

Context. Over the next few years, ALMA and Herschel missions will perform high spatial and spectral resolution studies at infrared and sub-millimeter wavelengths. This will provide much greater detail about the composition and evolution of molecules in space. Modeling of the spectra will require accurate radiative and collisional rates for species of astrophysical interest. Aims. We calculate ro-vibrational excitation rate coefficients of SO by He, useful for studies of high-temperature environments. Methods. A new accurate three dimensional (3D) potential energy surface was calculated for the SO-He system which explicitly takes into account the r-dependence of the SO vibration as well as the R-distance and 6 angle which describe the relative position of the collision partners. The dynamics calculations were performed according to the VCC-IOS approximation. Results. The new rate coefficients between the ro-vibrational levels are calculated for temperatures from 300 K to 800 K.

Ab initio potential-energy surface and rovibrational states of the HCN-HCl complex

A four-dimensional intermolecular potential-energy surface has been calculated for the HCN-HCl complex, with the use of the coupled cluster method with single and double excitations and noniterative inclusion of triples. Data for more than 13,000 geometries were represented by an angular expansion in terms of coupled spherical harmonics; the dependence of the expansion coefficients on the intermolecular distance R was described by the reproducing kernel Hilbert space method. The global minimum with De=1565 cm(-1) and Re=7.47a0 has a linear HCN-HCl hydrogen-bonded structure with HCl as the donor. A secondary hydrogen-bonded equilibrium structure with De=564 cm(-1) and Re=8.21a0 has a T-shaped geometry with HCN as the donor and the acceptor HCl molecule nearly perpendicular to the intermolecular axis. This potential surface was used in a variational approach to compute a series of bound states of the isotopomers HCN-H35Cl, DCN-H35Cl, and HCN-H37Cl for total angular momentum J=0,1,2 and spectroscopic parities e, f. The results could be analyzed in terms of the approximate quantum numbers of a linear polyatomic molecule with two coupled bend modes, plus a quantum number for the intermolecular stretch vibration. They are in good agreement with the recent high resolution spectrum of Larsen et al. [Phys. Chem. Chem. Phys. 7, 1953 (2005)] in the region of 330 cm(-1) corresponding to the HCl libration. The (partly anomalous) effects of isotopic substitutions on the properties of the complex were explained with the aid of the calculations.

Dynamical manifestation of Hamiltonian monodromy

Hamiltonian monodromy —a topological property of the bundle of regular tori of a static Hamiltonian system which obstructs the existence of global action-angle variables— occurs in a number of integrable dynamical systems. Using as an example a simple integrable system of a particle in a circular box with quadratic potential barrier, we describe a time-dependent process which shows that monodromy in the static system leads to interesting dynamical effects.

Ab initio rovibronic states of the thioketenyl radical in its X2Π electronic ground state

We present an ab initio study of the thioketenyl (HCCS) radical in its degenerate X(2)Π electronic ground state. All rotational and vibrational degrees of freedom are taken into account including the electronic orbital and spin angular momenta. The structure of the rovibronic levels and the nature of the corresponding wave functions show resonances even at very low energies due to strong couplings between the bending, rotation, and spin terms in the Hamiltonian. Assignments from the dominant contributions of the eigenvectors are discussed in parallel with previously published data. The rotational structures for the first excited vibronic states are computed as well as transition intensities for the fundamental one.

Rovibronic spectroscopy of the van der Waals complex He–HCl+

The potential energy surfaces and the calculated rovibronic spectrum of the electronic ground state of the van der Waals He–HCl+ cation are presented. The system is in a X 2Π electronic state at linearity, which splits into an A′ and an A″ state upon bending, leading to a Renner–Teller effect. Three-dimensional potential energy surfaces have been determined using the partially spin-restricted open-shell single and double excitation coupled cluster method with perturbative triples [RCCSD(T)]. The absolute minimum of a two-dimensional surface with the diatom bond length r fixed at r e = 2.489 a 0 is located at the linear He–HCl+ geometry with a van der Waals bond length R of 5.98 a 0 and D e ≃ 300 cm−1. The minimum in the full three-dimensional potential occurs for a slightly larger value of r: 2.492 a 0. The rovibronic levels of the He–HCl+ complex have been computed by a variational method for total angular momenta J =1/2, 3/2, 5/2, 7/2 and 9/2. The binding energy D 0 is calculated as 161.5 cm−1 using the two-dimensional potential energy surfaces with r frozen at r e and as 163.5 cm−1 in full three-dimensional calculations. Owing to the large and negative value of the spin–orbit parameter in HCl+ (A SO = −648.13 cm−1), all the considered rovibronic states correspond to the |Ω| = 3/2 spin–orbit component of HCl+. The nuclear wave functions of the complex could be interpreted using the model of a slightly hindered diatomic rotor. The energy level pattern and wave functions have been compared with the more floppy Ar–OH complex on the one hand and the more rigid He–HF+ system on the other. The anisotropy of the potential energy surface of the He–HCl+ complex is intermediate between these two cases and the rovibronic states reflect this property.

Symbolic Interpretation of the Molien Function: Free and Non-free Modules of Covariants

A mathematical problem originating from molecular physics leads to the exploration of the algebraic structures of sets of multivariate polynomials whose variables are the (x i, y i) components of n vectors in a plane with a common origin. The symmetry is assumed to be described by the SO(2) Lie group. The irreducible representations (irreps) of the group are labeled by the integer m. The ring of invariants is the set of polynomials that transform under the action of the SO(2) group according to the m = 0 irrep. Such a ring admits a Cohen–Macaulay decomposition. The set of polynomials changing as the (m) irrep, m ≠ 0, under the elements of the group defines the module of (m)-covariants. The module of (m)-covariants is free when |m| < n and the expression of the Molien function is symbolically interpreted in terms of a standard integrity basis containing one set of denominator polynomials and one set of numerator polynomials. In contrast, the module of (m)-covariants is non-free when |m| ≥ n and a generalized integrity basis has to be introduced to throw light on the Molien function. A graphical representation of the algebraic structures of the free and non-free modules is proposed.