Variable-screening method for diatomic molecules

A variable-screening method is proposed for the calculation of electronic energies of diatomic molecules. This new method is applied to the ground state of HeH⁺ in order to investigate its utility.     

Variable-screening model for diatomic molecules

An effective hamiltonian method based on a one-electron potential is proposed. The potential is represented by a sum of two coulombic interactions with effective nuclear charges depending upon the internuclear distance. This potential preserves the separability of Schrödinger equation. The method can be usefully applied to various atom (ion)-atom collision problems. Calculations are carried out for some states of HeH⁺ and HeH using one configuration built up from a minimal basis set chosen to ensure correct dissociation.     

Maximum-entropy analysis of momentum densities in diatomic molecules

The one-particle density in momentum space γ(p) is studied for diatomic molecules by using the maximum-entropy technique. The knowledge of one or more momentum expectation values <p"> provides approximations on the density γ(p) for any value of the momentum, which are convergent when increasing the number of known moments. Other unknown expectation values are estimated in terms of the constructed maximum-entropy densities. A numerical study of the quality of the approximations is carried out by means of experimental and theoretical data for the momentum expectation values involved. Experimental errors are also taken into account to have an idea of the sensibility of the results to the information from which they are obtained. © 1997 John Wiley & Sons, Inc.     

Coherent states for anharmonic diatomic molecules

In this work, we construct approximate coherent states for a Morse‐like potential using the displacement operator method and a method recently proposed by Gazeau and Klauder. To test if these states are minimum uncertainty states, we evaluate the temporal evolution of the dispersions in position and momentum. We also construct the trajectories in the phase space and compare with the classic solution. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Potential surface crossings for diatomic molecules

We study the nonradiative processes in diatomic molecules produced by a potential surface crossing in terms of a generalized optical potential containing an absorptive and a resonant part. The theory is applicable to inelastic atomic scattering, predissociation, accidental predissociation and collisionally induced dissociation. The coupling term between the electronic surfaces (in the diabatic representation) is evaluated semiclassically in terms of the “inelastic action” s. While the Landau–Zener formula is obtained from a linearized function of s, a more realistic form is proposed as a rational fraction in s.     

Improved multiparameter exponential-type potential for diatomic molecules

We report an improved multiparameter exponential-type potential (MPETP) energy model for diatomic molecules. It is found that this potential is identical to the Tietz potential in the realm of diatomic molecules. The efficiency of the improved MPETP is clarified by simulating the internuclear interaction potential curve for the A (³Π₁) state of the chlorine monofluoride molecule.     

Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001     

Thermal dissociation of diatomic molecules

The establishment of equilibrium in the chemical reaction X₂+M 2X+M is examined. All possible transitions between the vibrational levels and the continuous spectrum are considered. Taking account of two relaxation times, an expression is obtained for the concentration of the X atoms and the chemical reaction rate as a function of time. The conditions under which the dependence of the chemical reaction rate on time acquires an exponential nature are determined. An expression free from the requirement that the initial concentrations of X-atoms and X₂ molecules should be close to their equilibrium values is obtained for the rate constant.In conclusion, the authors thank Prof. N. D. Sokolov for discussion of the work.     

Thermal decomposition of diatomic molecules

A conjugate kinetic equation is used, which reduces to the Focker-Planck equation for heavy molecules. Equations are derived for the mean dissociation time and for higher moments of the distribution. It is shown that for heavy diatomic molecules the mean time alone need be considered in the region of high energy barriers. Use of the conjugate kinetic equation is also considered when the model corresponds to a quantized oscillator, the mean dissociation time being obtained as the solution to a system of algebraic equations.We are indebted to N. N. Tunitskii for interest in the work, and to E. V. Stupochenko and M. N. Safaryan for discussions on the results.     

Stochastic dissociation of diatomic molecules

The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focusing on their dissociation probabilities. It is found that the quantum system is more robust than the classical one in the limit of a large number of kicks. The opposite behavior emerges for a small number of kicks. Quantum and classical dissociation probabilities do not coincide for any parameter combinations of the force. This can be attributed to a scaling property in the classical system which is broken quantum mechanically.     

Simplifications of spin-rotation parameters for homonuclear diatomic molecules

Spin-rotation parameters for homonuclear diatomic molecules are simplified and applied to the np ³Π_u Rydberg series of H₂. A model of spin-rotation is derived by dividing the electron distribution into core- and Rydberg-like terms.     

Rydberg-London potential for diatomic molecules and unbonded atom pairs

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.     

Periodic tables of diatomic and triatomic molecules

The Mendeleev periodic table of atoms is one of the most important principles in natural science. However, there is shortage of analog for molecules. Here we propose two periodic tables, one for diatomic molecules and one for triatomic molecules. The form of the molecular periodic tables is analogous to that of Mendeleev periodic table of atoms. In the table, molecules are classified and arranged by their group number G, which is the number of valence electrons, and the periodic number P, which represents the size of the molecules. The basic molecular properties, including bond length, binding energy, force constant, ionization potential, spin multiplicity, chemical reactivity, and bond angle, change periodically within the tables. The periodicities of diatomic and triatomic molecules are thus revealed. We also demonstrate that the periodicity originates from the shell-like electronic configurations of the molecules. The periodic tables not only contain free molecules, but also the "virtual" molecules present in polyatomic molecules. The periodic tables can be used to classify molecules, to predict unknown molecular properties, to understand the role of virtual molecules in polyatomic molecules, and to initiate new research fields, such as the periodicities of aromatic species, clusters, or nanoparticles. The tables should be of interest not only to scientists in a variety of disciplines, but also to undergraduates studying natural sciences.     

二原子分子和三原子分子的周期表

门捷列夫元素周期表是自然科学中最重要的原则之一．然而,对于分子而言,却缺乏类似的表格．本文提出两个分别对应于二原子分子和三原子分子的周期表．这些分子周期表的格式和门捷列夫原子周期表相似．在这些表格中,分子依照它们各自的族数G和周期数P分类排列,G是价电子的数目而P则表示分子的尺寸．分子的基本性质,包括键长、结合能、力常数、电离势、自旋多重度、化学反应活性以及键角等等,都随着表中的G和P作周期性的变化．二原子分子和三原子分子的周期性因而被揭示开来．本文还进一步指出这种周期性是源出于分子的壳状电子构型．周期表中不仅包含了游离的分子,还包含了多原子分子中的“赝”分子．这些周期表可用来从本质上分类分子,广泛地预言分子的未知性质,了解在多原子分子中赝分子的作用,以及开拓新的研究领域,如芳香族、团簇或纳米微粒的周期性等．因此这些表格不仅能够引起多学科领域中科学工作者的关注,而且还能引起理科学生们的兴趣．     

The generalized potential energy function for diatomic molecules

A new generalized potential energy function is suggested for diatomic molecules. The Dunham, Simons—Parr—Finlan, Thakkar and Ogilvie potentials are shown to be particular cases of the generalized potential energy function. It is also shown that the function suggested may reproduce the path of the potential curve with sufficient accuracy even for the cases of small expansion length.     

Electric dipole polarity of diatomic molecules

The restricted SCF (single-configuration SCF) and MCSCF (multiconfiguration SCF) calculations are performed to compute the ground-state electric dipole moments of four pairs of diatomic molecules—(1) CO and BF; (2) SiO and AlF; (3) CS and BCl; and (4) SiS and AlCl—at a number of internuclear distances on both sides of the equilibrium position. Near Hartree–Fock accuracy is obtained in the SCF calculations. All eight molecules have a range of internuclear distance in which electric dipole moments are of the polarity of A^?B⁺. The shapes of computed electric dipole moment functions are discussed in the language of the molecular orbital method and in relationship to electronegativities of atoms. The present study gives us deeper understanding of electron transfer inside molecules and consequently of the apparent contradiction between electronegativity and the dipole polarity of some molecules. © John Wiley & Sons, Inc.