Evaluation of Vibrational Energies by Means of Neural Networks

A program for neural networks was developed to evaluate many vibrational energies of harmonic oscillators, Morse oscillators and diatomic molecules. The tests of all the vibrational levels of SiH (A state) and HF (B state) with v_max equal to 8 and 31, respectively, yielded results in excellent agreement with semi-empirical Morse results. The program was also applied to the three vibrational modes of H₂O accurately.     

基态NS、SiF的旋轨耦合常数的非经验计算

分子的自旋轨道耦合常数对分析分子光谱的精细结构有重要意义。Richards等^[1]自七十年代起利用Hartree-Fock波函数,非经验地计算了一些分子的旋轨耦合常数,获得了与实验值吻合的结果。本文报导利用我们发展的计算程序,对两个基态分子NS(X²Π),SiF(X²Π)进行了旋轨耦合常数的计算,其结果与实验符合良好。     

Symmetry aspects of diatomics-in-molecules (DIM) calculations. II. Construction of symmetry-adapted diatomic fragment subspaces

A new general procedure is presented for the construction of symmetry adapted diatomic fragment sub-spaces of spin-adapted polyatomic DIM bases obtained by direct diagonalization of the polyatomic spin-square operator. The spin part of the construction is accomplished by the diagonalization in the DIM basis of the diatomic spin-square operators. The spatial part of relevant transformations is given in terms of quantum numbers of the constituent atomic functions. Simple expressions for the spatial symmetry and spin designation of the resulting symmetry-adapted diatomic fragment states are obtained. Special attention is paid to consistent phases of diatomic fragment functions corresponding to equivalent fragments. The approach eliminates such mental operations from the construction of symmetry-adapted diatomic fragment subspaces which are difficult to formulate in a way suitable for straightforward computer implementation.     

FORTRAN routine to compute Born–Oppenheimer potential energy curves directly from spectroscopic data

A computer program that calculates Born–Oppenheimer potential energy curves of diatomic molecules directly from spectroscopic data is presented. Rather than performing the usual preliminary fitting of the experimental data to a single polynomial in the variable (v + 1/2), where v is the vibrational quantum number, the program contains an accurate built-in interpolation routine by which each experimental input point belongs to its own polynomial. The program is tested on the ground state of the H₂ molecule and results are compared with the most accurate ab initio calculations available. © 1993 John Wiley & Sons, Inc.     

Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules

We present the implementation of a variational finite element solver in the HelFEM program for benchmark calculations on diatomic systems. A basis set of the form is used, where (μ, ν, φ) are transformed prolate spheroidal coordinates, B _n(μ) are finite element shape functions, and are spherical harmonics. The basis set allows for an arbitrary level of accuracy in calculations on diatomic molecules, which can be performed at present with either nonrelativistic Hartree-Fock (HF) or density functional (DF) theory. Hundreds of DFs at the local spin density approximation (LDA), generalized gradient approximation (GGA), and the meta-GGA level can be used through an interface with the Libxc library; meta-GGA and hybrid DFs are not available in other fully numerical diatomic program packages. Finite electric fields are also supported in HelFEM , enabling access to electric properties. We introduce a powerful tool for adaptively choosing the basis set by using the core Hamiltonian as a proxy for its completeness. HelFEM and the novel basis set procedure are demonstrated by reproducing the restricted open-shell HF limit energies of 68 diatomic molecules from the first to the fourth period with excellent agreement with literature values, despite requiring orders of magnitude fewer parameters for the wave function. Then, the electric properties of the BH and N₂ molecules under finite field are studied, again yielding excellent agreement with previous HF limit values for energies, dipole moments, and dipole polarizabilities, again with much more compact wave functions than what were needed for the literature references. Finally, HF, LDA, GGA, and meta-GGA calculations of the atomization energy of N₂ are performed, demonstrating the superb accuracy of the present approach.     

The rational fraction representation of diatomic potentials

The representation of diatomic potential energy curves by rational fractions using low order polynomials in numerator and denominator is investigated. The rational fraction method, which is illustrated by examples, is shown to fail in providing a robust representation of diatomic potentials for wide application.     

双原子位点M-N-C电催化剂在CO2还原反应中活性位点的最佳分布

双原子位点M-N-C催化剂是催化CO₂还原反应(CO₂RR)性能最佳的催化剂之一. 然而, 目前的研究主要集中于M-N-C活性中心原子类型的调控, 低估了活性位点的配位模式及分布对其催化性能的影响. 本文选取典型的双原子位点M-N-C催化剂(NiFe-N-C)为研究对象, 采用密度泛函理论方法探究了9种活性位点具有不同配位环境的NiFe-N-C催化剂电催化CO₂RR的反应机理. 结果表明, 随着金属原子配位数、 双原子位点间距离的增加, M-N-C催化剂的稳定性、 催化CO₂还原至CO的活性及抑制氢析出反应的选择性均呈现先升高后下降的趋势. 其中, 金属原子四配位且对称分布的NiFe-N-C-model 3催化剂, 因其双原子位点的强相互作用表现出最优的催化性能.     

“Neglect of Diatomic Differential Overlap” in nonempirical quantum chemical orbital theories. III. On the spectrum of the overlap matrix for diatomic molecules over locally orthogonalized basis functions

The sum of the smallest and the greatest eigenvalue of the overlap matrix of diatomic molecules in a basis of locally orthogonalized linearly independent functions is equal to 2. Therewith, polynomial expansion techniques for the justification of the NDDO approximation become identical for diatomic molecules. © 1995 John Wiley & Sons, Inc.     

Application of potential constants: Empirical determination of molecular energy components for diatomic molecules

The potential (force) constant of a diatomic molecule is applied to determine the molecular energy components such as the electronic kinetic (T) and electrostatic potential (V) energies. The theoretical framework of the method is constructed from T and V representations of the quantum mechanical virial theorem. To confirm the utility of the method developed here, the calculated molecular energy components of diatomic molecules are compared with available Hartree-Fock data. It is concluded that the present method is simple and powerful for evaluating the molecular energy components of various diatomic molecules.     

Interference caused by indium in the atomization of Ag, Bi, Cd, Sn, and Tl in ETA-AAS

The depression of the signals for Ag, Bi, Cd, Sn, and Tl trace determination by ETA-AAS, which occurs in the presence of hydrobromic acid (with or without indium present), has been investigated by use of a new combined atomization equipment, molecular absorption measurements and thermodynamic calculations. The results show that all these elements form easily volatile bromides and more or less stable diatomic molecules of MBr type. These diatomic molecules, formed in the gaseous phase, are removed from the observation volume by diffusion, before their dissociation is complete. These two effects-formation of easily volatile compounds and stable diatomic molecules-are the main reasons for the depression of the atomic-absorption signals.     

Time-Dependent quantum theory. IV. Effect of lattice relaxation on the optical spectra

The absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line-width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue-shift of the absorption spectrum and a red-shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over-all shape, of the emission line calculated here with those observed in the Vegard–Kaplan band of N₂ dissolved in rare gas crystals is discussed.     

Time-dependent quantum theory III. Model for vibrational relaxation in crystals

A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range. An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 10⁴ sec ^?;1. The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm ^?1 at ⁰K. An explanation for the thermal quenching of the low-temperature luminescence of SO₂ is based upon induced cascade-phonon emission.     

Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.     

Coherent and incoherent orientation and alignment of ICN photoproducts

We report extended measurements of the rotational polarization and correlated angular distribution of CN photofragments from ICN photodissociation, with a particular emphasis on the creation and detection of molecular orientation with circularly-polarized light. Doppler profiles of the nascent photoproducts are measured by Frequency-Modulated (FM) transient absorption, and the resulting high signal-to-noise data are valuable for verifying the form of the angular correlations between the recoil velocity, the photofragment rotational angular momentum, and the space-fixed frame defined by the dissociation polarization. A space-fixed bipolar moment notation can be used for an unambiguous characterization of the maximal set of polarization properties that can be created with one-photon excitation and detected with one-photon Doppler-resolved absorption spectroscopy. Relating the observed polarization moments to the various coherent and incoherent, adiabatic and non-adiabatic mechanisms, that have been derived and verified extensively in the case of diatomic photodissociation to polarized atomic fragments, is not unambiguous in the case of diatomic fragments from triatomic precursors. Constraints among various polarization moments confirmed in the case of diatomic dissociation are not confirmed in this triatomic case, where the perpendicular transitions to non-degenerate A' and A' components of a linear Omega = 1 state are qualitatively different from excitation to degenerate Omega = +/-1 states in a diatomic molecule.     

An energy criterion for determiningd orbital contribution to adsorbate bonding to a transition metal: CO/Fe12

Summary A new criterion is presented for determining the contribution of a particular class or group of orbitals to a chemical bond. The new criterion is the diatomic energy contribution of particular orbitals to a bond. In neglect to differential overlap methods the total energy may be decomposed entirely into monoatomic and diatomic terms. The contribution of the electrons ind orbitals to the diatomic energy terms, which are responsible for holding a molecule together, have been calculated for an Fe-Fe bond of Fe₁₂ and for the Fe-C bond of CO absorbed at an on-top site of an Fe₁₂ cluster. This direct measure of thed electron contribution to the total energy indicates that thed orbitals are responsible for only a small contribution to the Fe-Fe binding energy and to the binding energy for absorbed CO. This occurs, despite there being larged orbital attractive diatomic energy terms, because a careful analysis indicates repulsive terms balance the attractive terms.     

Controlling dynamics in diatomic systems

Controlling molecular energetics using laser pulses is exemplified for nuclear motion in two different diatomic systems. The problem of finding the optimized field for maximizing a desired quantum dynamical target is formulated using an iterative method. The method is applied for two diatomic systems, HF and OH. The power spectra of the fields and evolution of populations of different vibrational states during transitions are obtained.     

The complete T-->V,R energy conversion in three-body collisions within the hard sphere model

It is shown that in hard sphere (impulsive) collisions of atoms with diatomic molecules, complete conversion of the collision energy into the internal energy of the diatomic partner is possible for any number of impacts between the elastic balls representing the particles. The corresponding collision geometries and relations between the masses of the particles are described in detail.     

Dynamics of adsorption: A model calculation for HD activated adsorption

We have recently developed a model potential for the interaction of a diatomic molecule with a rigid solid surface. In this note, we report some results of classical trajectory studies designed to simulate the adsorption of a diatomic molecule. Model potentials with different barrier heights are used and a variety of different initial conditions for the incident molecule are studied. In common with gas-phase results, we find that translational energy is most effective in surmounting early barriers and enhancing adsorption.     

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.