scholarly journals Фундаментальный анализ сингулярных и резонансных явлений в колебательных полиадах молекулы дифторсилилена

2020 ◽  
Vol 128 (12) ◽  
pp. 1795
Author(s):  
С.В. Краснощеков ◽  
Е.О. Добролюбов ◽  
Сюаньхао Чан
Keyword(s):  
Energy Surface ◽  
Branch Points ◽  
Vibrational States ◽  
Real Numbers ◽  
Fourth Degree ◽  
Normal Coordinates ◽  
Quartic Potential ◽  
Fortran Language ◽  
Unit Radius ◽  
Schrödinger Perturbation

The singular structure of the lower vibrational states of the difluorosilylene molecule (up to four quanta of total excitation) was studied by expanding the energies of each state in the series of high-order Rayleigh-Schrödinger perturbation theory and analyzing their implicit multivalued properties using the fourth degree Padé-Hermite approximants. The quartic potential energy surface in dimensionless normal coordinates was calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of the values of multivalued approximants reproduces the variational solution with high accuracy, while other values, starting from the fourth polyad, in many cases coincide with the energies of other states of the polyad. The Fermi and Darling-Dennison resonances are analyzed on the basis of the coincidence of the singular complex branch points of the approximants for interacting states inside or near a circle of unit radius on the complex plane. It was found that a pair of states can have several coinciding branch points of solutions, including those inside the unit circle. It is concluded that this approach is an effective method for determining the polyad structure of vibrational states. The calculation parameters are selected, which are necessary for the reproducibility of key results. The calculations were carried out using a software package in the Fortran language using a package of arithmetic calculations with a long mantissa of real numbers (200 digits).

Energies and Electric Dipole Moments of the Bound Vibrational States of HN2+ and DN2+

2008 ◽  
Vol 73 (6-7) ◽  
pp. 873-897 ◽  
Author(s):  
Vladimír Špirko ◽  
Ota Bludský ◽  
Wolfgang P. Kraemer
Keyword(s):  
Dipole Moment ◽  
Nearest Neighbor ◽  
Energy Surface ◽  
Dipole Moments ◽  
Three Dimensional ◽  
Vibrational States ◽  
Spacing Distribution ◽  
Triatomic Molecules ◽  
Vibrational Levels ◽  
Different Levels

The adiabatic three-dimensional potential energy surface and the corresponding dipole moment surface describing the ground electronic state of HN2+ (Χ1Σ+) are calculated at different levels of ab initio theory. The calculations cover the entire bound part of the potential up to its lowest dissociation channel including the isomerization barrier. Energies of all bound vibrational and low-lying ro-vibrational levels are determined in a fully variational procedure using the Suttcliffe-Tennyson Hamiltonian for triatomic molecules. They are in close agreement with the available experimental numbers. From the dipole moment function effective dipoles and transition moments are obtained for all the calculated vibrational and ro-vibrational states. Statistical tools such as the density of states or the nearest-neighbor level spacing distribution (NNSD) are applied to describe and analyse general patterns and characteristics of the energy and dipole results calculated for the massively large number of states of the strongly bound HN2+ ion and its deuterated isotopomer.

scholarly journals Progress in calculating the potential energy surface of H 3 +

2012 ◽  
Vol 370 (1978) ◽  
pp. 5001-5013 ◽  
Author(s):  
Ludwik Adamowicz ◽  
Michele Pavanello
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Molecular Geometry ◽  
Computational Procedure ◽  
Energy Functional ◽  
Basis Functions ◽  
Vibrational States ◽  
Energy Gradient ◽  
Explicitly Correlated

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh–Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H rovibrational spectrum is reproduced at the 0.1 cm −1 accuracy level up to 16 600 cm −1 above the ground state.

scholarly journals Study of the Vibrational Predissociation of the NeBr2 Complex by Computational Simulation Using the Trajectory Surface Hopping Method

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2029
Author(s):  
Ernesto García-Alfonso ◽  
Maykel Márquez-Mijares ◽  
Jesús Rubayo-Soneira ◽  
Nadine Halberstadt ◽  
Kenneth C. Janda ◽  
...  
Keyword(s):  
Energy Surface ◽  
Computational Simulation ◽  
Kinetic Mechanism ◽  
Experimental Methods ◽  
Classical Dynamics ◽  
Vibrational States ◽  
Surface Hopping ◽  
Vibrational Predissociation ◽  
New Information ◽  
Rotational Distribution

The vibrational predissociation of NeBr2 has been studied using a variety of theoretical and experimental methods, producing a large number of results. It is therefore a useful system for comparing different theoretical methods. Here, we apply the trajectory surface hopping (TSH) method that consists of propagating the dynamics of the system on a potential energy surface (PES) corresponding to quantum molecular vibrational states with possibility of hopping towards other surfaces until the van der Waals bond dissociates. This allows quantum vibrational effects to be added to a classical dynamics approach. We have also incorporated the kinetic mechanism for a better compression of the evolution of the complex. The novelty of this work is that it allows us to incorporate all the surfaces for (v=16,17,…,29) into the dynamics of the system. The calculated lifetimes are similar to those previously reported experimentally and theoretically. The rotational distribution, the rotational energy and jmax are in agreement with other works, providing new information for this complex.

Some Properties of a Quartic Potential with a Finite Binding Energy

1978 ◽  
Vol 33 (12) ◽  
pp. 1581-1587
Author(s):  
R. N. Kesarwani ◽  
Y. P. Varshni
Keyword(s):  
Binding Energy ◽  
Potential Energy ◽  
Energy Function ◽  
Interparticle Distance ◽  
Potential Energy Function ◽  
Vibrational States ◽  
Third Order ◽  
Quartic Potential ◽  
The Third ◽  
Range Of Values

Abstract A potential energy function is proposed which exhibits a quartic dependence on (r - re), where re is the equilibrium interparticle distance, in the neighbourhood of re, and has a finite binding energy. To study the pattern of the eigenvalues, the WKBJ method is applied to the third order, and the relevant integrals are evaluated analytically. Results are shown graphically for a few sets of parameters. The number of vibrational states that the potential can support is determined for a range of values of the parameters. Some suggestions as to the possible applications of the proposed potential are also made.

Exact solutions of a quartic potential

2019 ◽  
Vol 34 (26) ◽  
pp. 1950208 ◽  
Author(s):  
Qian Dong ◽  
Guo-Hua Sun ◽  
M. Avila Aoki ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Exact Solutions ◽  
Quantum System ◽  
Analytical Solutions ◽  
Wave Functions ◽  
Negative Potential ◽  
Potential Parameter ◽  
Real Numbers ◽  
Quartic Potential ◽  
Heun Functions ◽  
Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

Variational calculations of vibrational states of N2O using hyperspherical normal coordinates

1996 ◽  
Vol 105 (15) ◽  
pp. 6099-6110 ◽  
Author(s):  
José Zùñiga ◽  
Mercedes Alacid ◽  
Adolfo Bastida ◽  
Alberto Requena
Keyword(s):  
Vibrational States ◽  
Normal Coordinates ◽  
Variational Calculations

A first-principles potential energy surface and vibrational states for hydrogen on Cu(100)

2004 ◽  
Vol 121 (15) ◽  
pp. 7434-7439 ◽  
Author(s):  
Wenzhen Lai ◽  
Daiqian Xie ◽  
Jinlong Yang ◽  
Dong Hui Zhang
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
First Principles ◽  
Energy Surface ◽  
Vibrational States

Analytical expressions for the energies of anharmonic oscillators

2000 ◽  
Vol 78 (9) ◽  
pp. 845-850
Author(s):  
F M Fernández ◽  
R H Tipping
Keyword(s):  
Perturbation Parameter ◽  
Bound State ◽  
Perturbation Series ◽  
Simple Expression ◽  
Branch Points ◽  
Anharmonic Oscillators ◽  
Large Coupling ◽  
Analytical Behavior ◽  
Schrödinger Perturbation ◽  
Analytical Expressions

We propose a systematic construction of algebraic approximants for the bound-state energies of anharmonic oscillators. The approximants are based on the Rayleigh-Schrödinger perturbation series and take into account the analytical behavior of the energies at large values of the perturbation parameter. A simple expression obtained from a low-order perturbation series compares favorably with alternative approximants. Present approximants converge in the large-coupling limit and are suitable for the calculation of the energy of highly excited states. Moreover, we obtain some branch points of the eigenvalues of the anharmonic oscillator as functions of the coupling constant. PACS No.: 03.65Ge

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