Configuration localized wave functions: General formalism and applications to vibrational spectroscopy of diatomic molecules (original) (raw)
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Accurate ro-vibrational spectroscopy of diatomic molecules in a Morse oscillator potential
Results in Physics, 2013
This work presents the bound-state spectra of Morse oscillator, which remains one of the oldest important model potentials for molecules. Accurate ro-vibrational energies are obtained by means of a generalized pseudospectral method that offers an optimal, non-uniform discretization of the radial grid. Both swave (' = 0) and rotational (' -0) states for low and high quantum numbers are calculated for four representative diatomic molecules, namely H 2 , LiH, HCl and CO. First nine states belonging to a maximum of n, ' = 2 are computed with good accuracy, along with nine other high-lying states for each of these molecules. Present results surpass the accuracy of all hitherto published calculations found so far, except the tridiagonal J-matrix method, which produces similar accuracy as ours. Detailed variation of energies with respect to state indices n, ' shows interesting behavior. A host of new states including the higher ones are reported as well. This offers a simple general efficient scheme for calculating these and other similar potentials in molecular physics.
Ro-vibrational studies of diatomic molecules in a shifted Deng-Fan oscillator potential
International Journal of Quantum Chemistry, 2014
Bound-state spectra of shifted Deng-Fan oscillator potential are studied by means of a generalized pseudospectral method. Very accurate results are obtained for both low as well as high states by a non-uniform optimal discretization of the radial Schrödinger equation. Excellent agreement with literature data is observed in both s-wave and rotational states. Detailed variation of energies with respect to potential parameters is discussed. Application is made to the ro-vibrational levels of four representative diatomic molecules (H 2 , LiH, HCl, CO). Nine states having {n, ℓ} = 0, 1, 2 are calculated with good accuracy along with 15 other higher states for each of these molecules.
The Journal of Chemical Physics, 2000
We have recently presented a formalism for calculating zero-point vibrational corrections to molecular properties of polyatomic molecules in which the contribution to the zero-point vibrational correction from the anharmonicity of the potential is included in the calculations by performing a perturbation expansion of the vibrational wave function around an effective geometry. In this paper we describe an implementation of this approach, focusing on computational aspects such as the definition of normal coordinates at a nonequilibrium geometry and the use of the Eckart frame in order to obtain accurate nonisotropic molecular properties. The formalism allows for a black-box evaluation of zero-point vibrational corrections, completed in two successive steps, requiring a total of two molecular Hessians, 6K -11 molecular gradients, and 6K -11 property evaluations, K being the number of atoms. We apply the approach to the study of a number of electric and magnetic properties-the dipole and quadrupole moments, the static and frequency-dependent polarizability, the magnetizability, the rotational g tensor and the nuclear shieldings-of the molecules hydrogen fluoride, water, ammonia, and methane. Particular attention is paid to the importance of electron correlation and of the importance of the zero-point vibrational corrections for obtaining accurate estimates of molecular properties for a direct comparison with experiment.
A General Algebraic Model for Molecular Vibrational Spectroscopy
Annals of Physics, 1996
We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions.
Systematic Approach to Compute the Vibrational Energy Levels of Diatomic Molecules
Journal of Applied Mathematics and Physics, 2020
In continuation of our previous paper of the anharmonic potentials analysis through the Floquet representation, we performed in this work a systematic calculation of the diatomic vibrational energy levels as well as the corresponding wave functions. The solution of Schrödinger equation according to Morse potential, which is a suitable model to describe the diatomic vibrational spectra, has been introduced; thus the explicit formulas to the second order have been established. As an illustration, the dissociation energies of some molecules species (i.e. ScN, LiH, Cl 2 and NO) have been computed, as well as the wave functions and the corresponding probability densities, relating to the (ScN) molecule have been represented. Comparisons of our results with those of literature have been made.
Calculation of the vibrational wave function of polyatomic molecules
The Journal of Chemical Physics, 2000
A modified perturbation approach for the calculation of the vibrational wave function of polyatomic molecules is discussed. It is demonstrated that if the expansion point of the potential is determined variationally, the leading first-order term in the perturbation expansion of the vibrational wave function vanishes. Furthermore, the new expansion point is a very good approximation to the vibrationally averaged molecular geometry. The required third derivatives of the potential energy with respect to geometrical distortions have been calculated by numerical differentiation. Two approaches are discussed, one based on the differentiation of the molecular Hessian and the other on the molecular gradient. Results are presented for the averaged molecular geometry of a large set of molecules, including studies of electronically excited states and effects of electron correlation. The largest molecule included is butane with a total of 14 atoms.
Ro-vibrational spectroscopy of molecules represented by a Tietz–Hua oscillator potential
Journal of Mathematical Chemistry, 2014
Accurate low and high-lying bound states of Tietz-Hua oscillator potential are presented. The radial Schrödinger equation is solved efficiently by means of the generalized pseudospectral method that enables optimal spatial discretization. Both ℓ = 0 and rotational states are considered. Rovibrational levels of six diatomic molecules viz., H 2 , HF, N 2 , NO, O 2 , O + 2 are obtained with good accuracy. Most of the states are reported here for the first time. A detailed analysis of variation of eigenvalues with n, ℓ quantum numbers is made. Results are compared with literature data, wherever possible. These are also briefly contrasted with the Morse potential results. *
Anharmonic vibrational eigenfunctions and infrared spectra from semiclassical molecular dynamics
The Journal of chemical physics, 2018
We describe a new approach based on semiclassical molecular dynamics that allows simulating infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power spectra by computing first the vibrational eigenfunctions as a linear combination of harmonic states, and then the oscillator strengths associated with the vibrational transitions. We test the approach against a 1D Morse potential and apply it to the water molecule with results in excellent agreement with discrete variable representation quantum benchmarks. The method does not require any grid calculations, and it is directly extendable to high dimensional systems. The usual exponential scaling of the basis set size with the dimensionality of the system can be avoided by means of an appropriate truncation scheme. Furthermore, the approach has the advantage to provide IR spectra beyond the harmonic approximation without losing the possibility of an in...
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 symmetry adapted approach to molecular spectroscopy: the anharmonic oscillator symmetry model
1996
We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in D 3h and T d molecules. A systematic procedure can be used to establish the relation between the algebraic and configuration space formulations, by means of which new interactions are found in the algebraic model, leading to reliable spectroscopic predictions. We illustrate the method for the case of D 3h -triatomic molecules and the T d Be-cluster.