Exchange Perturbation Theory Research Articles

Collisional broadening and shift of the hyperfine lines for complex atomic systems in atmosphere of the buffer inert gases

An effective approach to determination of the collisional hyperfine lines shift and broadening in a buffer gas medium is presented and based on the generalized kinetic theory of spectral lines, the exchange perturbation theory and relativistic gauge-invariant perturbation theory with the optimized model potential approximation for computing the optimized basises of the relativistic wave functions.The results of calculating the shift and broadening of the hyperfine structure spectral lines due to collisions for complex atoms (here thallium is considered) in an atmosphere of inert gases (Kr, Xe) are presented and compared with other available alternative theoretical and experimental data. It is shown that the ratio of an adiabaticbroadening to a collisional shift for the pair of Tl–Kr (Га/р)/ fр is ~1/75 and for the pair of Tl- Xe(Га/р)/fр ~1/60.These estimates testify to a violation of well-known Foley relationship, which is, as a rule, inviolable in the standard atomic spectroscopy.

RELATIVISTIC SPECTROSCOPY OF ATOMIC SYSTEMS: SPECTRAL LINES BROADENING AND SHIFT FOR HEAVY ELEMENTS IN THE BUFFER GAS AND PLASMAS ENVIRONMENT

It has been developed a modified relativistic approach to describing the shift and broadening due to collisions of spectral lines of hyperfine structure for alkali atoms in an atmosphere of buffer (inert) gases. The approach is based on the generalized kinetic theory of spectral lines, exchange, relativistic perturbation theory with the Dirac-Hartree-Slater zeroth approximation and accounting for the complicated correlation effects by means of using the many-body polarization density-dependent functionals. The basic expressions for the collision shift and broadening hyperfine structure spectral lines are taken from the kinetic theory of spectral lines. The exchange perturbation theory (the modified version ЕL-НАV) has been used to calculate the corresponding potentials. The results of calculating the interatomic potentials, local shifts, temperature dependent spectral line shifts for the systems of the Rb, Cs-He are listed and compared with available theoretical and experimental data. The important feature of our scheme is correct taking into account the correlation (polarization) effects with using special effective functionals from. The difference between our theoretical data and other calculation results can be explained by using different perturbation theory versions and different approximations for calculating the wave functions basis’s.

Permutation Symmetry in Coherent Electrons Scattering by Disordered Media

A non-Anderson weak localization of an electron beam scattered from disordered matter is considered with respect to the principle of electron indistinguishability. A weak localization of electrons of a new type is essentially associated with inelastic processing. The origin of inelasticity is not essential. We take into account the identity principle for electron beam and electrons of the atom of the scatterer with an open shell. In spite of isotropic scattering by each individual scatterer, the electron exchange contribution has a hidden parameters effect on the resulting angular dependence of the scattering cross-section. In this case, the electrons of the open shell of an atomic scatterer can be in the s-state, that is, the atomic shell remains spherically symmetric. The methods of an invariant time-dependent exchange perturbation theory and a Green functions with exchange were applied. An additional angular dependence of the scattering cross-section appears during the coherent scattering process. It is shown exactly for the helium scatterer that the role of exchange effects in the case of a singlet is negligible, while for the triplet state, it is decisive, especially for those values of the energy of incident electrons when de Broglie’s waves are commensurate with the atomic.

Peculiarities of a helium interaction with hydrogen and free electrons from the point of view of the exchange perturbation theory solutions

We consider an adiabatic potential of a Hydrogen-Helium interaction by using a new approach based on the exchange perturbation theory (EPT). This method allows to present results analytically. We find the solution as an expansion in an antisymmetric basis thanks to the proved completeness property for a nonorthogonal set of antisymmetric wave functions. We use the developed invariant form with respect to interatomic electron permutations for both the Hamiltonian describing an unperturbed system and the perturbation operator. The invariant form for both operators allows one to obtain properly antisymmetric corrections to the antisymmetric wave function of the zero approximation. The probability of electron scattering with electron capture by the helium atom is discussed. We use an EPT formalism developed for the time-dependent perturbations. A formalism of the Time-dependent EPT has a form of an invariant perturbation theory that accounts for intercentre electron permutations among the overlapping states. The expressions for the matrix elements of an S-matrix and a T-matrix account for interatomic electron permutations. We use the obtained differential cross section formulas for the description of the electron capture during the scattering processes. The differential cross section of the electron capture by Helium atom has a complex shape of peak for the scattering energy around 0.7 atomic units, associated with the adiabatic creation of the negative ion He(-1).

OPTIMIZED RELATIVISTIC DIRAC-FOCK APPROACH TO CALCULATING THE HYPERFINE LINE SHIFT AND BROADENING FOR HEAVY ATOMS IN THE BUFFER GAS

It is presented a new consistent relativistic approach to description of the energetic and spectral properties of the heavy atoms in an atmosphere of the inert gases, based on the atomic gauge-invariant relativistic perturbation theory with the optimized Dirac-Fock zeroth approximation with density functional correlation potential and the exchange perturbation theory for construction of the interatomic potential function. As illustration it is applied to calculating the interatomic potentials, hyperfine structure line collision shift and broadening for alkali and thallium atoms, in an atmosphere of the buffer inert gas. It is shown that an accurate accounting of relativistic and exchange-correlation provides physically reasonable description of the energetic and spectral properties of the heavy atoms in an atmosphere of the inert gases.

NEW RELATIVISTIC APPROACH TO CALCULATING THE HYPERFINE LINE SHIFT AND BROADENING FOR HEAVY ATOMS IN THE BUFFER GAS

It is presented a new consistent relativistic approach to hyperfine structure line collision shift and broadening for heavy atoms in an atmosphere of the buffer inert gas, based on the atomic gauge-invariant relativistic perturbation theory and the optimal construction of the interatomic potential function within exchange perturbation theory. As illustration it is applied to calculating the interatomic potentials, hyperfine structure line collision shift for heavy atoms in an atmosphere of the buffer inert gas. The accurate account for the relativistic and exchange-correlation and continuum pressure effects is necessary for an adequate description of the energetic and spectral properties of the heavy atoms in an atmosphere of the heavy inert gases.

Scattering of proton by Lithium atom with electron exchange

SynopsisWe present formalism of Time-dependent Exchange Perturbation Theory (TDEPT) built to all orders of perturbation, for arbitrary time dependency of perturbation and apply it to the problem of proton scattering on Lithium atom where we calculate the differential and the total cross-sections

Invariant time-dependent exchange perturbation theory and its application to the particles collision problem

We present the formalism of time-dependent exchange perturbation theory built to all orders of perturbation, for the arbitrary time dependency of perturbation. The theory takes into account the rearrangement of electrons among centers. We show how the formalism can be reduced to the standard form of invariant perturbation theory by “switching off” the re-arrangement of electrons among centers. The elements of the scattering S-matrix and transitions T-matrix and the formula for the electron scattering differential cross section are derived. The application of the theory to scattering and collision problems is discussed. As an example, we apply the theory to proton scattering on a lithium atom, calculating the differential and total cross sections.

Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations

A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework.

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La1/3Ca2/3MnO3 that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites.

Exchange Perturbation Theory for Multiatomic Electron System and Its Application to Spin Arrangement in Manganite Chains

A new methodology of binding energy calculation with respect to different spin arrangements for a multiatomic electron system is developed from the first principle in the frame of the exchange perturbation theory (EPT). We developed EPT formalism in the general form of the Rayleigh‐Srchödinger expansion with a symmetric Hamiltonian, taking into account an exchange and nonadditive contributions of a superexchange interaction. The expressions of all corrections to the energy and wave function were reduced to the nonsymmetric Hamiltonian form. The EPT method is extended for the case of degeneracy in the total spin of a system. As an example of the application of the developed EPT formalism for the degeneracy case, spin arrangements were considered for the key 〈Mn〉–O–〈Mn〉 (〈Mn〉: Mn3+ or Mn4+) fragments in manganites. In 〈Mn〉–O–〈Mn〉 for La1/3Ca2/3MnO3 are in good agreement the obtained estimations of Heisenberg parameter and binding energy with the available experimental data.

Can there be a convergent perturbation theory of intermolecular energies?

We investigate the relationship between the convergence of Rayleigh-Schrödinger perturbation theory and the degree of correspondence between the eigenvalues and eigenfunctions of a Hamiltonian Ȟ and those of a zero-order Hamiltonian Ȟ0. We show that the radius of convergence of the perturbation expansion that transforms Ψ01, the lowest energy eigenfunction of Ȟ0, into Ψj, the jth lowest eigenfunction of Ȟ, is less than the magnitude of the reciprocal of the largest magnitude eigenvalue of a particular Hermitian operator. The operator depends on Ȟ and Ȟ0. This result is used to derive a sufficient condition for the perturbation expansion to have a radius of convergence less than one when Ψ01 is a good approximation to Ψj. When we apply the condition to our exchange perturbation theory calculations on HeH+, we find that the expansion must have a radius of convergence less than one. For this system, Ψ01 is a very good approximation to Ψ2. A radius of convergence less than one for the HeH+ calculations implies that the expansions diverge or that they are converging to a state other than Ψ2. We briefly consider the implications of our studies for the existence of a convergent perturbation theory of intermolecular energies.

Primitive exchange perturbation theory, IV

The formalism which Certain and the author developed is summarized. For electron exchange problems this is equivalent to a generalization of the author's work with Silbey. It is suggested that good values of the energy may be calculated by a simple approximation which does not involve any exchange functions.

Spin depolarizing effect in collisions with neutral hydrogen

Aims. We develop an accurate and general semi-classical formalism that deals with the definition and the calculation of the collisional depolarizing constants of the levels of simple and complex singly-ionized atoms in arbitrary s -states perturbed by collisions with hydrogen atoms. The case of ions with hyperfine structure is investigated fully. Methods. We obtain potential energy curves based on the MSMA exchange perturbation theory by employing the Unsold approximation. These potentials enter the Schrodinger equation to determine the collisional T -matrix elements in a semi-classical description. We use the T -matrix elements for the calculation of the collisional depolarization rates of simple atoms. Then, we use these rates to calculate the collisional coefficients in cases of ions with hyperfine structure. Results. We evaluate the collisional depolarization and polarization transfer rates of the ground levels of the ionized alkaline earth metals $\ion{Be}{ii}$, $\ion{Mg}{ii}$, $\ion{Ca}{ii}$, $\ion{Sr}{ii}$, and $\ion{Ba}{ii}$. We study the variation of the collisional rates with effective principal quantum number n * characterizing an arbitrary s -state of a perturbed simple ion. We find that the collisional rates for simple ions obey simple power laws as a function of n * . We present direct and indirect formulations of the problem of the calculation of the depolarization and polarization transfer rates of levels of complex atoms and hyperfine levels from those for simple atoms. In particular, the indirect method allows a quick and simple calculation with its simple power-law relations. For the state 4s 2 S 1/2 of $\ion{Ca}{ii}$, our computed rate of the destruction of orientation differs from existing quantum chemistry calculations by only 4% at $T=5000$ K.

Binding Energies and Structures of NaI−(CH3CN)n=1-9 Clusters: Theoretical Study of the Contact Ion Pair versus the Solvent-Separated Ion Pair Structures in a Molecular Cluster

We present a theoretical study of the charge separation of NaI clustered with acetonitrile molecules. A model potential specially devised for the NaI−(CH3CN)n system has been built up according to the exchange perturbation theory as developed by Claverie. The potential energy surface (PES) exploration has been carried out using the Monte Carlo growth method (MCGM) at different fixed internuclear NaI distances, to obtain a minimum energy profile for the NaI bond breaking. From four to nine solvent molecules, the NaI−(CH3CN)n PES exhibits two local minima along the NaI internuclear distance. The first one is related to the contact ion pair (CIP) structure and the second where the two ions are separated by two or three acetonitrile molecules in a solvent-separated ion pair (SSIP) structure. With less than eight solvent molecules, the CIP configurations have the highest binding energies, but for nine acetonitrile molecules, the configurations where the two ions are separated by 7 Å have a higher binding energy than those where the two ions stay in contact (2.85 Å), reflecting an evolution from the CIP to the SSIP structures with the cluster size. This can be related to a recent gas phase photoionization experiment on NaI−(CH3CN)n and leads to the same conclusion: the charge separation of NaI should be achieved within a cluster containing fewer than 10 acetonitrile molecules.

The method of exchange perturbation theory as applied to magnetic ordering in high-T c materials

We unify the method of exchange perturbation theory for multicenter systems. For the case of exchange degeneracy in the total spin of the system we give a secular equation that is more compact and convenient for calculations than those obtained earlier. On the basis of this formalism we develop an algorithm for calculating the Heisenberg parameter for magnetic materials. Finally, we calculate the characteristics of antiferromagnetic transitions for the high-T c materials La2−x MeCuO4 and YBa2Cu3O6.

On the crystal structure problem for heavy rare-gas solids: A three-atom exchange perturbation analysis

The observed higher stability of a face-centered cubic (fcc) arrangement of atoms in heavy rare-gas solids, relative to that of a hexagonal close-packed (hcp) structure, is ascribed to the effect of three-atom short-range (exchange) interactions on the static lattice energy, evaluated in first- and second-order exchange perturbation theory. The summations are limited to 66 isosceles triangles with two atoms nearest neighbors of a central atom in the solid. Highly accurate results are reported, in part supplementing those of early work. An approach is taken in which the electrons of each atom are replaced by one electron on a Gaussian orbital with characteristic parameter β chosen such as to reproduce the attractive part of a Lennard-Jones (6, 12) pair potential, thus implicitly including intra- and inter-atomic electronic correlations. The results, for a wide range of values for the dimensionless parameter βR ( R is the nearest-neighbour distance in the solid at ambient pressure), invariably favor the fcc lattice, with a difference between fcc and hcp amounting to 0.4% of the total pair cohesive energy for solid argon, krypton and xenon (solid neon is a border case in thisanalysis). Recent papers on the crystal stability of rare-gas solids are critically examined.

Laser induced fluorescence of jet-cooled non-conjugated bichromophores: bis-phenoxymethane and bis-2,6-dimethylphenoxymethane

Abstract The electronic spectroscopy of bichromophoric molecules linked by a OCH 2 O chain, such as bis-phenoxymethane (1), and bis-2,6-dimethylphenoxymethane (3), has been studied in a supersonic free jet by laser induced fluorescence. The experimental results have been compared to calculations resting on the perturbative CIPSI method, in which the di- and tri-excited configurations involving the π as well the v orbitals have been taken into account. The bis-phenoxymethane (1) molecule shows a single 0—0 transition which is blue-shifted relative to anisole by more than 400 cm −1 . This blue-shift has been theoretically related to the conformation of the bichromophore which displays an out-of-plane distorsion of the ether chain relative to anisole. The calculations clearly show that the observed blue-shift of the transition is related to this distorsion, and not to any electronic coupling between both cycles which is very weak. The single transition experimentally observed corresponds to the most stable structure of (1) which is in a gauche-gauche conformation relative to the CO bonds of the chain. In this structure the cycles are equivalent. The study of van der Waals complexes of (1) with usual solvents confirms this interpretation and shows that the equivalence of the cycles is removed by complexation. This contrasts with the bichromophore (3) whose 0—0 transition is blue-shifted by only 25 cm −1 relative to the 2,6-dimethylanisole subunit. Calculations have shown that in this case, the monomeric subunit as well as the bichromophore are in an out-of-plane conformation due to the steric hindrance introduced by the methyl groups. Moreover the excited state of (3) behaves as a weakly fluorescent exciplex whereas the emission resulting from the excitation of (1) is resonant. For the sake of comparison, the fluorescence excitation spectrum of the van der Waals dimer of anisole has also been studied and exhibits a red-shift with respect to bare anisole. The equilibrium geometry and the exciton coupling have also been calculated for the anisole van der Waals dimer, by means of the exchange perturbation theory.

Potential energy of magnesium atom-hydrogen molecule interaction and interdiffusion coefficient

The potential energy of intermolecular interaction is calculated by the quantum-mechanical exchange perturbation theory. The results are used to calculate the diffusion coefficient for magnesium vapor in hydrogen. The calculations agree with the experimental results.