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Hua Wei

Bio: Hua Wei is an academic researcher from Université de Montréal. The author has contributed to research in topics: Triatomic molecule & Hamiltonian (quantum mechanics). The author has an hindex of 7, co-authored 8 publications receiving 661 citations.

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TL;DR: In this paper, the authors used the discrete variable representation (DVR) to calculate vibrational energy levels of H2O and SO2 using a Hamiltonian written in terms of bond length and bond angle coordinates and their conjugate momenta.
Abstract: The discrete variable representation (DVR) is used to calculate vibrational energy levels of H2O and SO2. The Hamiltonian is written in terms of bond length–bond angle coordinates and their conjugate momenta. It is shown that although these coordinates are not orthogonal and the appropriate kinetic energy operator is complicated, the discrete variable representation is quite simple and facilitates the calculation of vibrational energy levels. The DVR enables one to use an internal coordinate Hamiltonian without expanding the coordinate dependence of the kinetic energy or evaluating matrix elements numerically. The accuracy of previous internal coordinate calculations is assessed.

338 citations

Journal ArticleDOI
TL;DR: In this article, a dipole moment function expanded in the three internal bond coordinates is calculated for the fundamental and overtone transitions of H2O up to approximately 18,000 cm−1.
Abstract: Vibrational intensities are calculated for the fundamental and overtone transitions of H2O up to approximately 18 000 cm−1. The intensities are determined from a dipole moment function expanded in the three internal bond coordinates. The expansion coefficients are computed ab initio at the second‐order Mo/ller–Plesset level of theory with a 6‐311G** basis set. Vibrational wave functions are calculated either from a three‐dimensional harmonically coupled anharmonic oscillator (HCAO) model which uses Morse oscillators to represent both the stretches and the bend of H2O, or from a variational calculation employing the best available potential energy surface and an exact kinetic energy operator. To obtain the most meaningful vibrational intensities we define dipole moment components using the Eckart embedding. Both the HCAO and the variational intensities agree quite well with the experimental results, which span eight orders of magnitude. From the calculations we predict that it may be possible to detect as yet unobserved vibrational transitions of H2O.

108 citations

Journal ArticleDOI
TL;DR: In this article, a discrete variable representation (DVR) is defined from a finite basis representation (FBR) where matrix elements of terms or factors in the kinetic energy operator are computed by quadrature.
Abstract: Probably the most important advantage of the discrete variable representation (DVR) is its simplicity. The DVR potential energy matrix is constructed directly from the potential function without evaluating integrals. For simple kinetic energy operators the DVR kinetic energy matrix is determined from transformation matrices and exact matrix representations of one‐dimensional kinetic energy operators in the original delocalized polynomial basis set. For complicated kinetic energy operators, for which matrix elements of terms or factors with derivatives must be calculated numerically, defining a DVR is harder. A DVR may be defined from a finite basis representation (FBR) where matrix elements of terms or factors in the kinetic energy operator are computed by quadrature but implicating quadrature undermines the simplicity and convenience of the DVR. One may bypass quadrature by replacing the matrix representation of each kinetic energy operator term with a product of matrix representations. This product appr...

63 citations

Journal ArticleDOI
TL;DR: In this article, the exact Eckart embedded Radau kinetic energy operator was presented for calculating and analysing ro-vibrational spectra, which can be used to calculate and analyse the rovibrations.

51 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derive expressions to relate any Eckart axis system with two axes in the molecular plane to simple molecule-fixed axis systems commonly used to derive kinetic energy operators.
Abstract: For triatomic molecules we derive expressions to relate any Eckart axis system with two axes in the molecular plane to simple molecule-fixed axis systems commonly used to derive kinetic energy operators. We express the orientation of an Eckart axis system in terms of Jacobi, Radau or bond coordinates.

50 citations


Cited by
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TL;DR: In this article, a high quality ab initio potential energy surface (PES) and dipole moment function (DPM) for water has been determined and an adjusted PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J⩽5 for H216O.
Abstract: We report on the determination of a high quality ab initio potential energy surface (PES) and dipole moment function for water This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J⩽5 for H216O The changes in the PES are small, nonetheless including an estimate of core (oxygen 1s) electron correlation greatly improves the agreement with the experiment Using this adjusted PES, we can match 30 092 of the 30 117 transitions in the HITRAN 96 data base for H216O with theoretical lines The 10, 25, 50, 75, and 90 percentiles of the difference between the calculated and tabulated line positions are −011, −004, −001, 002, and 007 cm−1 Nonadiabatic effects are not explicitly included About 3% of the tabulated line positions appear to be incorrect Similar agreement using this adjusted PES is obtained for the 17O and 18O isotopes For HD16O, the agreement is not as good, with a root-mean-square error of 025 cm−1 for line

1,067 citations

Journal ArticleDOI
TL;DR: The convergence of ab initio predictions to the one-and n-particle limits has been systematically explored for several conformational energy prototypes as mentioned in this paper, including the inversion barriers of ammonia, water, and isocyanic acid, the torsional barrier of ethane, and the E/Z rotamer separation of formic acid.
Abstract: The convergence of ab initio predictions to the one- and n-particle limits has been systematically explored for several conformational energy prototypes: the inversion barriers of ammonia, water, and isocyanic acid, the torsional barrier of ethane, the E/Z rotamer separation of formic acid, and the barrier to linearity of silicon dicarbide. Explicit ab initio results were obtained with atomic-orbital basis sets as large as [7s6p5d4f3g2h1i/6s5p4d3f2g1h] and electron correlation treatments as extensive as fifth-order Mo/ller–Plesset perturbation theory (MP5), the full coupled-cluster method through triple excitations (CCSDT), and Brueckner doubles theory including perturbational corrections for both triple and quadruple excitations [BD(TQ)]. Subsequently, basis set and electron correlation extrapolation schemes were invoked to gauge any further variations in arriving at the ab initio limit. Physical effects which are tacitly neglected in most theoretical work have also been quantified by computations of non...

644 citations

Journal ArticleDOI
TL;DR: In this article, a review of state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches is presented.
Abstract: In this article, we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) is represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as a sum of products. It then exploits the powerful...

410 citations

Journal ArticleDOI
TL;DR: A general variational method to calculate vibrational energy levels of polyatomic molecules without dynamical approximation based on a Lanczos algorithm, which does not require storage of the Hamiltonian matrix.
Abstract: We present a general variational method to calculate vibrational energy levels of polyatomic molecules without dynamical approximation. The method is based on a Lanczos algorithm, which does not require storage of the Hamiltonian matrix. The rate‐determining step of each Lanczos iteration is the evaluation of the product of the matrix and a trial vector. We use simple product basis functions and write the Hamiltonian as a sum of factorizable terms. With n one‐dimensional functions in each of f dimensions, the matrix‐vector product requires no more than cnf+1 multiplications for a single term involving c coordinates. Choosing a (potential optimized) discrete variable representation (DVR) in each dimension, the potential energy matrix is diagonal. The rate‐determining step is now the multiplication of a vector by the kinetic energy matrix and c is effectively (with rare exceptions) at most two. The nf+1 scaling holds for both diagonal and mixed second derivative operators. The method is directly applicable ...

362 citations