1,721,073 research outputs found
Comment on 'Variational calculations of vibrational energy levels for XY4 molecules: 2. Bending states of methane' [2002, Molec. Phys., 100, 1623]
No full textRovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. III. Global vs local axis system and angular coordinates
No full textWe study different parametrizations of the angular space of polyatomic molecules for an orthogonal description of the molecular geometry. Kinetic energy operators for pentatomic molecules, given by compact and computationally useful forms in a global and a local formulation of the axis system, are compared and discussed. A new decomposition of T for sequentially bonded pentatomic molecules in conjunction with a basis of Wigner and associated Legendre functions provides kinetic energy matrix elements which are free of singularities. Practical problems caused by an unusual volume element for a description involving only intervector (bending) angles are addressed. The corresponding rovibrational kinetic energy operators are derived for the two-vector body-fixed formulation. (C) 2000 American Institute of Physics. [S0021-9606(00)00445-1]
Discrete variable approaches to tetratomic molecules Part I: DVR(6) and DVR(3)+DGB methods
No full textWe present two discrete variable representation (DVR) based methods for the determination of the vibrational energy levels of tetratomic molecules. Both methods are designed for orthogonal internal coordinates in a body-fixed reference frame and make use of the DVR of three angular variables. The angular DVRs allow the construction of a fixed-angle three-mode Hamiltonian for the stretching vibrations. For each of the angular triples, the stretching eigenvalue problems are solved by employing 3D radial DVRs in the DVR(6) approach and real three-dimensional distributed Gaussian functions in the DVR(3) + DGB method. The angular degrees of freedom are taken sequentially into account in conjunction with a contraction scheme resulting from several diagonalization/truncation steps. Vibrationally averaged geometries, expectation values of rotational constants, and several adiabatic projection schemes developed in this work for tetratomic molecules are used to characterize the vibrational levels calculated by the DVR(6) and DVR(3) + DGB. (C) 2002 Elsevier Science B.V. All rights reserved
Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. II. Nonorthogonal descriptions of internal molecular geometry
No full textA rovibrational kinetic energy operator for a two-vector embedded reference frame is derived for general polyatomic molecules of arbitrary structure. New compact expressions for (T) over cap in terms of angular momentum and linear momentum vector operators are explicitly given for tri-, tetra-, and pentatomic molecules. The necessary actions for the evaluation of kinetic energy matrix elements in a standard rotation-angular basis are summarized. The structure of kinetic energy operators in the body-fixed formulation is explained with the help of Cartesian components of angular momentum and linear momentum vector operators. Kinetic energy operators for tetratomic molecules in a bisector embedded body-fixed formulation and for sequentially bonded pentatomic molecules are derived to show how to use our general result for diverse coordinate systems. (C) 2000 American Institute of Physics. [S0021-9606(00)00203-8]
Discrete variable approaches to tetratomic molecules Part II: application to H2O2 and H2CO
No full textWe have carried out large-scale calculations for accurate vibrational energy levels of formaldehyde and hydrogen peroxide. The discrete variable representations of the radial and angular coordinates are employed together with the contraction scheme resulting from several diagonalization/truncation steps. The global potential energy surface due to Carter et al. [J. Mol. Spectrosc. 90 (1997) 729] is used for H,CO and due to Koput et al. [J. Phys. Chem. A 102 (1998) 6325] for H2O2. For both molecules, the calculated vibrational energy levels are characterized by combining vibrationally averaged geometries and expectation values of rotational constants with several adiabatic projection schemes for automatic quantum number assignments. The energy levels of H,CO involving the excited v, and v, vibrations appear as resonances beyond the zero-order picture consisting of uncoupled 3D stretching and 2D bending modes. The torsional energy levels of H2O2 are studied in great detail and different energy patterns occurring below and above the cis barrier are discussed. Our full dimensional calculations for H2O2 have shown that the OH triad levels, 2nu(OH), are symmetry adapted local mode states. (C) 2002 Elsevier Science B.V. All rights reserved
On intervector angle descriptions and their numerical implementation for solving molecular problems
No full textThe angular parametrization comprising only bending angles is considered in detail. For tetratomic and pentatomic molecules, we first study the volume element, coordinate ranges, and parity-adapted basis functions. In contrast to the common belief, we show that the intervector angle description allows to uniquely specify the internal molecular geometry and to model tunneling through planarity. The redundant intervector angle and coordinate interdependences are explained by simple geometrical means. Principal difficulties arising from the interdependent coordinate ranges obstruct the numerical implementation of the description studied, since the angular basis functions are nonorthogonal and the overlap matrix may easily become ill-conditioned. For the symmetry-adapted representation, the origin of multiple solutions for the redundant coordinate is discussed. We additionally show that the redundant coordinate plays an important role by the characterization of the internal molecular geometry of pentatomic molecules described in terms of the cosines of the intervector angles. (C) 2003 American Institute of Physics
Converging multidimensional rovibrational variational calculations: the dissociation energy of (HF)(2)
No full textWe report large scale quantum mechanical calculations for the ground state energy E-0 and for the dissociation energy D-0 of the HF dimer on the SQSBDE potential energy surface of Quack and Suhm. A value of 4593.13 cm(-1) is obtained for E-0 by a large scale variational basis set expansion and confirmed by very accurate quantum Monte Carlo calculations giving E-0 of 4593.15 +/- 0.03 cm(-1). The noticeably higher ground state energies computed in previous variational studies are explained by the use of suboptimal HF eigenfunctions. The new estimated value of D-0 is 1058.00 cm(-1). (C) 2000 Elsevier Science B.V. All rights reserved
A theoretical investigation of the vibrational states of HCO2- and its isotopomers
No full textMaking use of the coupled cluster variant CCSD(T) and the aug-cc-pVQZ basis set a six-dimensional (6D) potential energy surface has been calculated for HCO2-, a fundamental organic anion. Therefrom, a variety of vibrational term energies and wavefunctions has been obtained by means of the discrete variable representation in an approach termed DVR(6). Calculated wavenumbers of the fundamentals of HCO2- and DCO2- agree with recent experimental values from neon matrix isolation IR spectroscopy within 15 cm(-1). The out-of-plane bending vibrations nu(4) are predicted at 1030 and 894 cm(-1). Moderately strong Fermi resonance interaction is calculated between vibrational states nu(1) and 2nu(4) of DCO2-. Excellent agreement with experiment (differences less than 0.7 cm(-1)) is observed for the C-13 and O-18 isotopic shifts. Accurate ground-state rotational constants are predicted for eight different isotopomers of the formate ion and the dissociation process HCO2- --> H- + CO2 is investigated in some detail, with the dissociation energy D-0 predicted to be 216 kJ mol(-1)
Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations
No full textPosterInternational audienceThe interdependence of the description of the internal geometry and the corresponding kinetic energy operatorTˆ is investigated in detail for a general n-atomic molecule. For both space-fixed and body-fixed reference frames compact expressions of Tˆ are derived which are applicable to any set of n21 translationally and rotationally invariant internal vectors in a spherical polar parametrization. Simple analytical forms are given for reduced masses and kinetic coupling constants, which are the only vector specific parameters in the final rovibrational kinetic energy expression. The kinetic energy assumes the most separable form for an entirely orthogonal set of internal vectors. A highly efficient computer program for the calculation of rovibrational spectra of tetratomic molecules has been developed on the basis of this formulation. Calculations on the HF dimer and the metastable molecule HOCO illustrate the accuracy and flexibility of this approach
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