Rotational energy levels and line intensities for 2S+1Λ-2S+1Λ and 2S+1(Λ ± 1)-2S+1Λ transitions in a diatomic molecule van der Waals bonded to a closed shell partner (original) (raw)
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The Journal of Chemical Physics, 2010
A procedure is investigated for assigning physically transparent, approximate vibrational and rotational quantum labels to variationally computed eigenstates. Pure vibrational wave functions are analyzed by means of normal-mode decomposition ͑NMD͒ tables constructed from overlap integrals with respect to separable harmonic oscillator basis functions. Complementary rotational labels J K a K c are determined from rigid-rotor decomposition ͑RRD͒ tables formed by projecting rotational-vibrational wave functions ͑J 0͒ onto products of symmetrized rigid-rotor basis functions and previously computed ͑J =0͒ vibrational eigenstates. Variational results for H 2 O, HNCO, trans-HCOD, NCCO, and H 2 CCO are presented to demonstrate the NMD and RRD schemes. The NMD analysis highlights several resonances at low energies that cause strong mixing and cloud the assignment of fundamental vibrations, even in such simple molecules. As the vibrational energy increases, the NMD scheme documents and quantifies the breakdown of the normal-mode model. The RRD procedure proves effective in providing unambiguous rotational assignments for the chosen test molecules up to moderate J values.
A method for using a single Kindependent grid for problems where otherwise a basis of associated Legendre functions or the corresponding K-dependent grids would be employed, specific&y for calculating the rotational-vibrational energy Ievels of a triatomic molecule, has been described and tested. K independence has been achieved by the incorporation of the weight functions of associated Legendre functions into the Hamiltonian. Exact analytical expressions, valid for any DVR basis, of the matrix elements of the ro~tion-bending kinetic energy operator (in terms of scattering coordinates f have been given. Simple numerical tests demonstrate that this new method is a useful ahemative to the methods proposed so far.
A new operator formulation of the many-electron problem for molecules
Theoretical and Experimental Chemistry, 1989
An n-electron operator ~, called a wave operator, is associated with a 2n-electron molecular wave function. Electron densities and energy are written in terms of ~ An equation defining an exact wave operator is found. Thus, a 2n-electron vector problem (for the wave function) is rigorously reduced to an n-electron operator problem. Conditions are formulated which guarantee that ~ corresponds to a state with a given spin. The" configuration-interaction problem is considered and methods of approximate construction of ~,~ are discussed. In particular, a matrix algorithm is proposed for calculations in the two-body approximation. A generalizaton of the approach to the case of systems with an odd number of electrons is given. The waveoperator model developed forms a general basis for construction of covariant electron models of molecules.
Computing electronic structures: A new multiconfiguration approach for excited states
Journal of Computational Physics, 2006
We present a new method for the computation of electronic excited states of molecular systems. This method is based upon a recent theoretical definition of multiconfiguration excited states (due to one of us, see M. Lewin, Solutions of the Multiconfiguration Equations in Quantum Chemistry, Arch. Rat. Mech. Anal. 171 (2004) 83-114). Contrarily to previously used methods, our algorithm always converges to a stationary state of the multiconfiguration model, which can be interpreted as an approximate excited state of the molecule.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2008
This is the second article in which we study the rotating Morse potential model for diatomic molecules using the tridiagonal J-matrix approach. Here, we improve further the accuracy of computing the bound states and resonance energies for this potential model from the poles of the S-matrix for arbitrary angular momentum. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian, which is included in the computations analytically without truncation. Our method has been applied to both the regular and inverted Morse potential with favorable results in comparison with available numerical data. We have also shown that the present method adds few significant digits to the accuracy obtained from the finite dimensional approach (e.g. the complex rotation method). Moreover, it allows us to handle easily both analytic and non-analytic potentials as well as 1/r singular potentials.
Collinear inelastic collisions of an atom and a diatomic molecule using operator methods
We calculate transition probabilities between vibrational levels of a diatomic molecule induced by an incident atom. Our prototype model is constructed treating the relative translation of the colliding species as a classical variable. The vibrational states of the diatomic molecule are treated quantum mechanically in terms of the evolution operator without involving wave functions. The corresponding equations of motion are coupled quasi-classically. For illustration purposes we present applications to the time dependence of transition probabilities for different initial and final states as well as a canonical ensemble of initial conditions. Calculamos probabilidades de transición entre estados vibracionales de una molécula diatómica inducidas por unátomo incidente. El modelo prototipo trata el movimiento de traslación relativo como una variable clásica. Los estados vibracionales de la molécula diatómica se tratan cuánticamente en términos del operador de evolución, sin involucrar funciones de onda. Las ecuaciones de movimiento correspondientes se acoplan cuasi-clásicamente. A manera de ilustración presentamos aplicaciones a la dependencia temporal de probabilidades de transición para diferentes estados inicial y final así como para un ensamble canónico de condiciones iniciales.
The Journal of Chemical Physics
An effective and general algorithm is suggested for variational vibrational calculations of N-atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the Eckart-Watson Hamiltonians of nonlinear or linear reference configuration. Second, with the help of an exact expression of curvilinear internal coordinates (e.g., valence coordinates) in terms of orthogonal, rectilinear internal coordinates (e.g., normal coordinates), any high-accuracy potential or force field expressed in curvilinear internal coordinates can be used in the calculations. Third, the matrix representation of the appropriate Eckart-Watson Hamiltonian is constructed in a discrete variable representation, in which the matrix of the potential energy operator is always diagonal, whatever complicated form the potential function assumes, and the matrix of the kinetic energy operator is a sparse matrix of special structure. Details of the sug...