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In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates. [ABSTRACT FROM AUTHOR]

A full-dimensional ab initio potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methane–argon complex using the GENIUSH computer program and the Smolyak sparse grid method. The full-dimensional computations make it possible to study the fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly-bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm−1 root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the 〈r〉0 methane structure. Allowing 10 basis functions for the methane fragment in a 12D computation performs much better than the 3D models by reducing the rms of the bound state vibrational energies to 0.07 cm−1. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens a route to the study of the role of dispersion forces in the excited methane vibrations and the energy transfer from the intra- to the intermolecular vibrational modes. [ABSTRACT FROM AUTHOR]

In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtμπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only ∼1.52 × 108 quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 1013 points. [ABSTRACT FROM AUTHOR]

In this paper we propose a new quadrature scheme for computing vibrational spectra and apply it, using a Lanczos algorithm, to CH3CN. All 12 coordinates are treated explicitly. We need only 157'419'523 quadrature points. It would not be possible to use a product Gauss grid because 33 853 318 889 472 product Gauss points would be required. The nonproduct quadrature we use is based on ideas of Smolyak, but they are extended so that they can be applied when one retains basis functions θn1(r1)...θnD(rD) that satisfy the condition α1n1 + ··· + αDnD <= b, where the αk are integers. We demonstrate that it is possible to exploit the structure of the grid to efficiently evaluate the matrix-vector products required to use the Lanczos algorithm. [ABSTRACT FROM AUTHOR]

The size of the quadrature grid required to compute potential matrix elements impedes solution of the vibrational Schrödinger equation if the potential does not have a simple form. This quadrature grid-size problem can make computing (ro)vibrational spectra impossible even if the size of the basis used to construct the Hamiltonian matrix is itself manageable. Potential matrix elements are typically computed with a direct product Gauss quadrature whose grid size scales as ND, where N is the number of points per coordinate and D is the number of dimensions. In this article we demonstrate that this problem can be mitigated by using a pruned basis set and a nonproduct Smolyak grid. The constituent 1D quadratures are designed for the weight functions important for vibrational calculations. For the SF6 stretch problem (D=6) we obtain accurate results with a grid that is more than two orders of magnitude smaller than the direct product Gauss grid. If D>6 we expect an even bigger reduction. [ABSTRACT FROM AUTHOR]

Objective: To evaluate, in vitro, the antimicrobial effect of ozone gas on strains of reference mutans streptococci and strains isolated from children at a high risk of developing caries. Method and Materials: A series of dilutions was obtained from a total of 41 strains, and the effect of ozone was determined for applications of 10, 20, and 40 seconds, as well as a control, in terms of the reduction of viable bacteria. Results: Ozone application for 10 and 20 seconds produced a significant reduction in the number of bacteria, inversely proportional to the bacterial concentration. When exposure lasted 40 seconds, no viable bacteria were obtained. Conclusions: Both time of application and initial bacterial concentration bear an influence on the antimicrobial effect of ozone on mutans streptococci. [ABSTRACT FROM AUTHOR]

Invasion of the maxillary sinus is a relatively frequent complication in dental implant treatment of patients with inadequate bone height in the posterior maxilla. This event usually occurs during surgery and sometimes produces sinusitis. There is a paucity of reports in the literature of implants migrating into the sinus cavity after a period of function. In the 2 clinical cases presented, an intraosseous apical movement of the implants was produced several years after placement of the implants. Hypotheses and possible mechanisms by which an implant may migrate into the maxillary sinus are described. [ABSTRACT FROM AUTHOR]

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A new, highly accurate ab initio ground-state intermolecular potential-energy surface (IPES) for the CO–N2 complex is presented. Thousands of interaction energies calculated with the CCSD(T) method and Dunning's aug-cc-pVQZ basis set extended with midbond functions were fitted to an analytical function. The global minimum of the potential is characterized by an almost T-shaped structure and has an energy of −118.2 cm−1. The symmetry-adapted Lanczos algorithm was used to compute rovibrational energies (up to J = 20) on the new IPES. The RMSE with respect to experiment was found to be on the order of 0.038 cm−1 which confirms the very high accuracy of the potential. This level of agreement is among the best reported in the literature for weakly bound systems and considerably improves on those of previously published potentials. [ABSTRACT FROM AUTHOR]

Phosgene (Cl2C=O) is extremely poisonous, underscoring the importance of accurate infrared detection. Here, the computed vibrational energy levels of phosgene are reported for the first time from a six-dimensional potential energy surface (PES) that was constructed from 25,000 single-point energy computations at the CCSD(T)/cc-pVTZ level of theory. The computed points were fit using a neural network method, and the resulting PES was employed in the determination of vibrational energies and wavefunctions. Bond coordinates were utilised in conjunction with a collocation method to minimise problems that arise from the complicated nature of the kinetic energy operator. The collocation method makes possible the computation of energy levels without integral evaluation, and without the need to solve a generalised eigenvalue problem. Moreover, it is built on a nondirect product-pruned basis that is much smaller than the direct product basis that would be required to obtain the same accuracy. [ABSTRACT FROM AUTHOR]