Rovibrational momentum densities of diatomic molecules in the rigid rotor-harmonic oscillator approximation

The rigid rotor-harmonic oscillator model in the momentum representation is used to examine the rovibrational momentum density of a diatomic molecule. The effects on this function of rotational and vibrational excitation, thermal averaging, and nuclear spin statistics are exhibited in calculations on N₂ and thehydrogen halides, and a brief comparison with electron momentum densities is made.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

Parent-molecule rotational depolarization of photofragment angular momentum distributions: diatomic and polyatomic molecules

We extend the A(q)(k) polarization-parameter model, which describes product angular momentum polarization from one photon photodissociation of polyatomic molecules in the molecular frame [J. Chem. Phys., 2010, 132, 224310], to the case of rotating parent molecules. The depolarization of the A(q)(k) is described by a set of rotational depolarization factors that depend on the angle of rotation of the molecular axis γ. We evaluate these rotational depolarization factors for the case of dissociating diatomic molecules and demonstrate that they are in complete agreement with the results of Kuznetsov and Vasyutinskii [J. Chem. Phys., 2005, 123, 034307] obtained from a fully quantum mechanical approach of the same problem, showing the effective equivalence of the two approaches. We further evaluate the set of rotational depolarization factors for the case of dissociating polyatomic molecules that have three (near) equal moments of inertia, thus extending these calculations to polyatomic systems. This ideal case yields insights for the dissociation of polyatomic molecules of various symmetries when we compare the long lifetime limit with the results obtained for the diatomic case. In particular, in the long lifetime limit the depolarization factors of the A(0)(k) (odd k), Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) for diatomic molecules vanish; in contrast, for polyatomic molecules the depolarization factors for the A(0)(k) (odd k) reduce to a value of 1/3, whereas for the Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) they reduce to 1/5.     

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.     

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.     

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.     

An analysis of SCF and geometry convergence for diatomic molecules

A geometry and SCF convergence study of Hartree-Fock calculations using the 6-31G* basis set is carried out on the set of all possible diatomic molecules formed from atoms with Z≤36. The utility of Hartree-Fock calculations using the smaller STO-3G basis set to improve the convergence behavior is demonstrated.      

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.     

Calculation of bond energies in diatomic molecules

Theoretical Chemistry Accounts - An extrapolation method is proposed for an approximative evaluation of covalent bonding powers of some elements from their electronegativity values. Using these...     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

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.     

Rovibrational spectra of bounded diatomic molecules

Spectra of a bounded diatomic molecule is studied numerically. Shifted Deng–Fan oscillator potential has been used to model the molecule. The accurate five‐point finite difference method has been used to solve the Schrödinger equation for rovibrational motion of the molecule. The energies of the bound states as well as free states of the molecule have been calculated. In addition, radial matrix elements like , n = 1, 2, and 3 have been calculated. These have been used to calculate the ‐pole static polarizabilities. The variation of bound state energies, matrix elements and ‐pole static polarizabilities with the boundary radius has also been studied. The Stark effect in case of this bounded system has also been investigated.     

Interelectronic angle densities of atoms in momentum space

For the 102 atoms from He to Lr in their ground states, the Hartree–Fock interelectronic angle densities,¯A(¯₁₂), in momentum space are reported, where ¯₁₂ is the angle between the momentum vectorsp₁ and p₂ of two electrons. In the first three atoms, He–Be, ¯A(¯₁₂) is found to be uniform independent of ¯₁₂, while in the remaining 99 atoms,¯A(¯₁₂) is larger for a large ¯₁₂ than for a small ¯₁₂. Accordingly, the average interelectronic angles in momentum space are 90° precisely for the three atoms and greater than 90° for the 99 atoms.     

Spin-orbit and spin-other-orbit interaction in diatomic molecules

The correct relativistic Pauli-Breit Hamiltonian for spin-orbit and spin-other-orbit interaction in atoms is adapted for use with diatomic molecules. The relation between the fundamental molecular Hamiltonian thus obtained and the phenomenological operator AL · S is investigated, and some theoretical considerations are made concerning Van Vleck's hypothesis of pure precession. A formula convenient for ab initio calculation of the spin-orbit coupling constant is derived, assuming the electronic functions to be represented by a Slater determinant of one-electron molecular orbitals. Finally a method for theoretical determination of the sign of the spin-orbit coupling constant is demonstrated by several examples.

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Zusammenfassung Der korrekte Pauli-Breit-Hamiltonoperator für die verschiedenen Spin-Bahn-Wechselwirkungen in Atomen wird der Anwendung bei zweiatomigen Molekülen angepaßt. Die Beziehung zwischen den so erhaltenen molekularen Hamiltonoperator und dem phänomenologisch begründeten Operator AL·S wird untersucht, und einige Überlegungen zur Van Vleckschen Hypothese reiner Präzession werden dargestellt. Eine Formel für die ab initio-Besprechung der Spin-Bahn-Kopplungs-Konstanten wird abgeleitet, wobei angenommen wird, daß die elektronische Wellenfunktion durch eine Slater-determinante dargestellt wird, die aus Ein-Elektronen-MO's aufgebaut ist. Schließlich wird eine Methode zur theoretischen Bestimmung des Vorzeichens der Spin-Bahn-Kopplungs-Konstanten an verschiedenen Beispielen demonstriert.

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Résumé L'hamiltonien relativiste de Pauli-Breit pour l'interaction spin-orbite dans les atomes est adapté pour être utilisé dans les molécules diatomiques. La relation entre l'hamiltonien moléculaire ainsi obtenu et l'opérateur phénoménologique AL · S est étudiée, et l'on effectue certaines considérations théoriques sur l'hypothèse de précession pure de Van Vleck. On déduit une formule convenable pour le calcul ab initio de la constante de couplage spin-orbite en supposant les fonctions électroniques représentées par un déterminant de Slater. Enfin, plusieurs exemples permettent de démontrer une méthode pour la détermination théorique du signe de la constante de couplage spin-orbite.