Elements of the third kind and the spin-dependent chemical force

A lively philosophical debate has lately arisen over the nature of elementhood in chemistry. Two different senses in which the technical term ELEMENT is currently in use by chemists have been identified, leaving chemistry open to the logical fallacy of equivocation. This paper introduces a third, more elemental candidate: the high-enthalpy short-lived unbonded atom. An enthalpy index based on free-atoms-as-elements is established, whereby one can monitor the degree to which an atom’s spin-based attractive force is implemented exo-enthalpically when the atom binds chemically to others. Enthalpy indexing shows that the strength of an atom’s attractive force is proportional to its spin angular momentum. Vibrational spectroscopy shows that the force varies inversely as the fourth power of the inter-atom distance. Both features differentiate the chemical force from the stronger electromagnetic force and from the weaker Van der Waals force.     

Isomorphic hamiltonian of a polyatomic system oscillating near a collinear reaction surface

The quantum mechanical isomorphic Hamiltonian of an N-atom system simulated by a linear semirigtd model is derived. Use of an extraneous angle allows one to avoid singularities in linear configurations, still taking advantage of the standard angular momentum technique.     

Statistical evaporation of rotating clusters. IV. Alignment effects in the dissociation of nonspherical clusters

Unimolecular evaporation in rotating, nonspherical atomic clusters is investigated using phase space theory in its orbiting transition state version. The distributions of the total kinetic energy release epsilon(tr) and the rotational angular momentum J(r) are calculated for oblate top and prolate top main products with an arbitrary degree of deformation. The orientation of the angular momentum of the product cluster with respect to the cluster symmetry axis has also been obtained. This statistical approach is tested in the case of the small eight-atom Lennard-Jones cluster, for which comparison with extensive molecular dynamics simulations is presented. The role of the cluster shape has been systematically studied for larger, model clusters in the harmonic approximation for the vibrational densities of states. We find that the type of deformation (prolate versus oblate) plays little role on the distributions and averages of epsilon(tr) and J(r) except at low initial angular momentum. However, alignment effects between the product angular momentum and the symmetry axis are found to be significant, and maximum at some degree of oblateness. The effects of deformation on the rotational cooling and heating effects are also illustrated.     

Electron correlation and Hund's rule

It is suggested that simple electronic shielding effects induced by wave function antisymmetrization tend to govern the energy ordering of singlet and triplet terms within a two-electron atomic configuration. This approach gives rise to the following alternating rule: For the term of greatest orbital angular momentum within a configuration, the triplet lies below the singlet. The energy ordering reverses for the term of next highest angular momentum, and continues to alternate with each change of one unit in the orbital angular momentum until the term of lowest angular momentum is reached. In an examination of over 600 energy levels of the elements and their ions, the alternating rule reliably orders singlet–triplet energy levels in some 90% of the cases.     

Multireference configuration interaction calculations for positronium halides

Multireference configuration interaction (MRCI) calculations of the positronium halides, PsF, PsCl, PsBr, and PsI, are carried out, to give positron ionization energies, positronium binding energies, and two-photon annihilation rates. All CI calculations consider only valence correlation effect with a frozen-core approximation, and use the orbitals with angular momentum up to 8. To incorporate the effects of many-body correlations in the energies and two-photon annihilation rates, the MRCI calculations are repeated with increasing reference configurations, and the full CI limits of these energies and annihilation rates are estimated. The contribution from orbitals having angular momentum greater than 8 to those values is also estimated. Relative to our previous single reference CI calculations, many-body correlation effects significantly increase the positron ionization energies, positronium binding energies, and two-photon annihilation rates. The structures of the positronium halides are also discussed.     

Modulation of NMR spin echoes in coupled systems

A new theoretical approach to NMR spin echoes is described. The xy magnetizations which correspond to the lines in the spectrum are dealt with directly, by the use of the angular momentum properties of Liouville space. This simplifies the calculations for the AB spin systems and opens the way to larger systems.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

1s22p3 and 1s22s23l, l = s,p,d, excited states of boron isoelectronic series from explicitly correlated wave functions

For some members of the boron isoelectronic series and starting from explicitly correlated wave functions, six low-lying excited states have been studied. Three of them arise from the 1s(2)2p(3) configuration, and the other three from the 1s(2)2s(2)3l, l = s,p,d, configurations. This work follows a previous one on both the 1s(2)2s(2)2p-(2)P ground state and the four excited states coming from the 1s(2)2s2p(2) configuration. Energies, one- and two-body densities in position space and some other two-body properties in position and momentum spaces have been obtained. A systematic analysis of the energetic ordering of the states as a function of the total orbital angular momentum and spin is performed in terms of the electron-nucleus and electron-electron potential energies and the role of the angular correlation is discussed. All calculations have been carried out by using the Monte Carlo algorithm.     

Symmetry assignment in the distributed Gaussian functions method to study homonuclear rotating trimers

An approximate method based on the use of distributed Gaussian functions (DGF) to describe the interparticle distances is employed to study the rovibrational spectrum of trimers. Rotational energy levels are obtained by assuming that vibration and rotation are separated. Thus, eigenstates of the Hamiltonian for the zero total angular momentum, J = 0, are used as basis set to solve the rotational Hamiltonian. A procedure to identify the corresponding symmetry character for the rovibrational bound states is proposed. The DGF approach is applied to the case of the rotating Ar₃ trimer. The reliability of the method is tested by comparison with results from an exact hyperspherical coordinate calculation for J = 0, 1 and 6.     

Magnetic circular dichroism measurements of the magnetisation properties of matrix-isolated species having spin angular momentum only

Magnetic circular dichroism has been used for the first time to study the magnetisation properties of some matrix-isolated species. The samples chosen for measurement have one, three, five and six unpaired electrons in their ground electronic states and, nominally, no orbital angular momentum. The experimental results follow the theoretical predictions very closely, but the nature of the magnetisation function is such that it is not easy to distinguish between different combinations of g-value and total spin angular momentum.     

Stabilization of cluster dimers by centrifugal effects

The influence of finite angular momentum on the stabilization of an (Ar₁₃)₂ cluster dimer in Ar₁₃+Ar₁₃ collisions is investigated with simulations and simple models. Local optimizations on the effective rovibrational potentialenergy surface show that the centrifugal effects favor the mechanical stability of strongly prolate shapes. Molecular dynamics simulations are performed to study the collisions between two Ar₁₃ subclusters. At low collisional energy and large impact parameter, trapping of the product cluster in its dimer-like configuration is found. For larger values of the angular momentum, the “molecular” cluster is found to remain in this dimer-like structure during the time of the simulation. Intermediate values of the angular momentum allow isomerization into more compact structures, but still dimer-like. Again, the final product appears as dynamically stable. All of these dimer-like products have the thermodynamical properties of a rotating rigid-like body. At high energy, unimolecular evaporation rates from collisional heating are calculated and comparisons with the predictions of the Rice, Ramsperger, Kassel (RRK) and Weisskopf models are discussed. Qualitative agreement with the simulations, in particular concerning the evolution of the rates versus angular momentum is found. The rates decrease when angular momentum is increased, especially when the total energy is low. Thus, the enhancement of the stability of the product cluster by centrifugal effects has also a statistical character.     

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.     

Introduction

The formalism for a configuration interaction approach is presented, in which explicit introduction of interelectronic coordinates into individual configurations is accomplished through the use of spherical Gaussian correlation factors. Formulas for all required matrix elements over these configurations are derived, and a computationally convenient algorithm to evaluate the matrix elements is presented. In addition, analysis of the form of the correlation factor shows that both angular and radial correlation can be obtained using spherical Gaussian correlation factors.     

Determination of the helicity of oriented photofragments

Equations to enable determination of the helicity (angular momentum orientation) of photofragments resulting from single-photon dissociation of an isotropic sample of molecules are presented. The symmetry of the photofragment distribution is illustrated by three-dimensional vector plots of the expectation values of projections of the fragment total angular momentum. Equations describing circular polarization of light in the spherical tensor basis are presented. Methods for the optical measurement of angular momentum orientation are discussed, including determination of the helicity of circularly polarized light by a quarter-wave plate or single Fresnel rhomb.     

Frame transformation relations for fluxional symmetric rotor dimers

The theory of frame transformation relation connecting body oriented angular momentum states and lab weakly coupled momentum states have been extended from rotor-electron to rotor-dimer systems. Coupling schemes are analyzed for weak and strong cases of correlation between lab and two different rotor body frames. It is shown that the frame transformation relation is a purely quantum effect at low angular momentum but an approach to a classical limit for high J. Symmetry analysis of frame transformation is compared to eigensolutions of model coupling Hamiltonian.     

Exact and approximate solutions to the one-center McMurchie–Davidson tree-search problem

We have attempted to optimize the cost (the total number of floating-point operations required) of using the McMurchie–Davidson R_NLMj recurrence relation. Rigorous solutions of the tree-search problem inherent in the cost minimization are given for total angular momentum L ≤ 7. For L ≥ 8, the rigorous search algorithm is prohibitively expensive, and we propose an approximate algorithm that generates highly optimized trees. Cost comparisons demonstrate that the present scheme is consistently superior to two others currently in use.