We report vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and contracted basis. Many of the levels of the two previous VR variational calculations differ significantly and differ also from those reported in this paper. We identify the source of and correct symmetry errors on the potential energy surfaces used in the previous calculations. VR has two equivalent equilibrium structures. By plotting wavefunction cuts, we show that two tunnelling paths play an important role. Using computed wavefunctions it is possible to assign many states and thereby to determine tunnelling splittings that are compared with their experimental counterparts.
Due to the ubiquity and importance of water, water dimer has been intensively studied.Computing the (ro-)vibrational spectrum of water dimer is challenging. The potential has 8 wells separated by low barriers which makes harmonic approximations of limited utility. A variational approach is imperative, but difficult because there are 12 coupled vibrational coordinate. In this paper, we use a product contracted basis, whose functions are products of intramolecular and intermolecular functions computed using an iterative eigensolver. An intermediate matrix $\bs{F}$ facilitates calculating matrix elements. Using $\bs{F}$, it is possible to do calculations on a general potential without storing the potential on the full quadrature grid. We find that surprisingly many intermolecular functions are required. This is due to the importance of coupling between inter- and intra-molecular coordinates. The full $G_{16}$ symmetry of water dimer is exploited. We calculate, for the first time, monomer excited stretch states and compare $P(1)$ transition frequencies with their experimental counterparts. We also compare with experimental vibrational shifts and tunnelling splittings. Surprisingly, we find that the the largest tunnelling splitting, which does not involve interchange of the two monomers, is smaller in the asymmetric stretch excited state than in the ground state. Differences between levels we compute and those obtained with a [6+6] adiabatic approximation [Leforestier et al. J. Chem. Phys. {\bf{137}} 014305 (2012) ] are $\sim 0.6$ cm$^{-1}$ for states without monomer excitation, $\sim 4$ cm$^{-1}$ for monomer excited bend states, and as large as $\sim 10$ cm$^{-1}$ for monomer excited stretch states.
An accurate ab initio ground-state intermolecular potential energy surface (PES) was determined for the CO-CO 2 Van der Waals dimer. The Lanczos algorithm was used to compute ro-vibrational energies on this PES. For both the C-in and the O-in T-shaped isomers, the fundamental transition frequencies agree well with previous experimental results. We confirm that the in-plane states previously observed are geared states. In addition, we have computed and assigned many other vibrational states. The rotational constants we determine from J = 1 energy levels agree well with their experimental counterparts. Planar and out-ofplane cuts of some of the wavefunctions we compute are quite different, indicating strong coupling between the bend and torsional modes. Because the stable isomers are T-shaped, vibration along the out-of-plane coordinates is very floppy. In CO-CO 2 , when the molecule is out-of-plane, interconversion of the isomers is possible, but the barrier height is higher than the in-plane geared barrier height.
By doing calculations on the methane-water Van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions and the Symmetry Adapted Lanczos (SAL) method. The Wigner D basis is a nondirect product basis and therefore efficient when the kinetic energy operator has accessible singularities. The SAL makes it possible to exploit symmetry to label energy levels and reduce the cost of the calculation, without explicitly using symmetry-adapted basis functions. Line strengths are computed and new bands are identified.
We introduce a new method for computing spectra of molecules for which a spin-spin term in the Hamiltonian has an important effect. In previous calculations, matrix elements of the spin-spin term and of the potential were obtained by expanding the potential and using analytic equations in terms of 3 − j symbols. Instead, we use quadrature. Quadrature is simple and makes it possible to do calculations with a general potential and without using the Wigner-Eckart theorem. In previous calculations, the Hamiltonian matrix was built and diagonalized. Instead, we use an iterative eigensolver. It makes it easy to work with a large basis. The ideas are tested by computing energy levels of NH(3 Σ −)-He, O 2 (3 Σ − g)-Ar and O 2 (3 Σ − g)-He.
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