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．     

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.     

Lie algebraic approach to Fermi resonance levels of CS2 and CO2

By using the general Hamiltonian based on the Lie algebraic method, the highly excited vibrational energy levels of linear triatomic molecules CS₂ and CO₂ are calculated, which proves that neglecting other perturbations and considering only 1:2 Fermi resonance, the obtained Hamiltonian can be used effectively to calculate the vibrational energy levels of linear triatomic molecules. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 154–161, 2001     

Highly excited vibrational levels of triatomic molecule N2O: U(4) algebraic model

In the U(4) algebraic framework, the triatomic molecules are of U₁(4) ? U₂(4) dynamical symmetry. A molecular Hamiltonian is constructed including the third‐order conbination of the invariant operators. Within this framework, the highly vibrational energy levels of the linear triatomic nitrous oxide molecule, including both bending and stretching vibrations, are studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Simple electrostatic models for vibrating unsymmetrical triatomic molecules and triatomic ions

Bond charge, point-dipole models are used to derive simple universal relations,K =0.0435 (K₁₁ K ₂₂)^1/2 –0.0086 (K ₁₁ ⁺ K ₂₂), andK = 0.11 (K ₁₁ K ₂₂)^1/2 –0.0055 (K ₁₁ +K ₂₂), between the bond stretching force constantsK ₁₁ andK ₂₂ and bond bending force constantK for linear and bent unsymmetrical triatomic molecules respectively. The relations are shown to be approximately valid for a number of molecules. An extension of the models to include charged species (ions) in triatomic molecules is also presented and tested, giving good results.Based on part of a thesis submitted by José L. Gázquez in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The Johns Hopkins University, 1976, and aided by research grants to the Johns Hopkins University and University of North Carolina from the National Institutes of Health and the National Science Foundation.     

Force constants of angle deformation in triatomic molecules

An expression for the angle deformation force constant of a polyatomic molecule has been derived on the basis of electrostatic theorem. By testing this expression with a number of triatomic molecules, it has been shown that the expression is useful for predicting the force constant of angle deformation in triatomic molecules.     

Bending force constant formulas from a bond-charge model of triatomic molecules

A bond-charge point-dipole model of molecular electronic structure is used to derive a general relation between the bending force constant, K_θθ, and stretching force constant , K₁₁, of linear and non-linear triatomic molecules.     

A Lie group method for molecular rovibrational spectra via the broken symmetry of U(r)(2)⊗U(υ)(4)

A special group chain that is appropriate for describing the rovibrational spectra of linear triatomic molecules with respect to both the vibration and the rotation of molecules as harmonic oscillators is given, and the corresponding Hamiltonian is constructed. The eigenvalue expression of the Hamiltonian is similar to the formula commonly used to calculate the rovibrational spectra of linear triatomic molecules. This method eliminates the physical uncertainty brought about by a variety of group chains. The relationships between parameters in the present expression and those in the commonly used expressions are given. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 53–59, 2001     

三原子分子振转激发态的理论研究

三原子分子振转激发态的理论研究谢代前,鄢国森,田安民（四川大学化学系,成都,６１００６４）关键词振转激发态,三原子分子,变分法能级较高的振转激发态通常包含大振幅运动,其波函数分布于很广的势能面区域内,传统的正则模理论已不适合于解决这类问题．近年来,Ｈ...     

Perimetric scale-shape coordinates for triatomic molecules

Perimetric nuclear coordinates of a triatomic molecule treat all three nuclei equivalently and are not subject to the triangle conditions. Through an appropriate orthogonal transformation they can be separated into one scale coordinate, viz., the circumference, and two shape coordinates, which are determined by the angles. The parameter space of the shape coordinates is an equilateral triangle. The basic formulas are given and the relationship between points in coordinate space and molecular shapes are elucidated. Received: 10 January 1996 / Accepted: 2 January 1997     

The geometrical-classical limit of algebraic Hamiltonians for molecular vibrotational spectra

A classical limit, which is amenable to a geometrical interpretation, is discussed for the vibron model of molecular vibrotational spectra. Both diatomic and triatomic molecules are considered. An example of a coupling between the two stretching modes of a linear triatomic is examined in detail.     

Triatom-triatom collisions: Fixed angle close-coupling study of vibrational excitation in the 12CO2+13CO2 system

A close-coupling approach to the calculation of quantal vibrational transition probabilities for the fixed angle scattering of a linear triatomic molecule with another linear triatomic molecule is described. The method is applied to the ¹²CO₂+¹³C0₂ collisional system. For a calculated inelastic transition probability to have an appreciable magnitude, it is found that the amount of energy transferred in a transition must be very small and just one quantum of energy must be exchanged between either the symmetric stretch or the asymmetric stretch vibrational modes of ¹²C0₂ and ¹³CO₂. For collisional energies away from threshold, the probabilities for transitions involving the symmetric stretch ¹²CO₂ and ¹³CO₂ modes are insensitive to long range multipole terms in the potential energy surface, while the probabilities for energy exchange between the asymmetric stretch modes are considerably diminished when the long range terms are removed from the potential energy surface. A brief discussion is presented on the possibilities of extending the technique to the calculation of vibrational excitation cross sections for three-dimensional triato—triatom collisions.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

Application of Lie algebraic method to the calculation of rotational spectra for linear triatomic molecules

The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.     

Force field description of the bending motion of triatomic molecules

A power series in the angular variable ρ = [sin (θ/2) - sin (θ_e/2)]/sin (θ_e/2) is shown to accurately describe the bending motions of triatomic molecules. Comparisons of force fields and ab-initio bending potentials are given.     

Hypervirial SCF treatment for vibrational energy levels of triatomic molecules

The SCF method for the calculation of energy levels of triatomic molecules is applied using the hypervirial perturbative procedure for solving the coupled equations. This treatment allows to obtain in a recursive way the energy corrections and the expectation values required in the SCF treatment, avoiding the explicit calculation of the wave functions. A numerical application is made to the SO₂ and O₃ molecules, comparing our results with those obtained by other methods.     

An Application of the Dynamical Lie Algebraic Method to Potential Energy Surface of the Stable Linear Asymmetric Tetratomic Molecules

Potential energy surfaces play an important role in studying theoretical chemistry. In the present paper, we first use the dynamical symmetry group G = U ₁(4) U ₂(4) U ₃(4) to get the expression of the potential energy surface for the stable linear asymmetric tetratomic molecules with the stretching vibration and the dissociation energy. The method can be applied to a number of stable tetratomic molecules. As an example we use the method to calculate the potential energy surface of C₂HD.     

Asymmetric dissociation of a symmetric molecule: Photofragmentation dynamics of Cd (CH3)2

A theoretical analysis of the dissociation of energy-rich triatomic molecules shows that asymmetric dissociation is expected to be the major decay mode. Both experimental and computational (classical trajectories) results for the photofragmentation of Cd(CH₃)₂ are in accord with the theoretical analysis.