Infinite-order Two-component Method Research Articles

Two-component transformation inclusive contraction scheme in the relativistic molecular orbital theory

The incorporation of a two-component transformation into the contraction coefficients of basis functions is suggested. Such a contraction, referred to as “two-component transformation inclusive contraction (TIC)”, effectively eliminates the computational cost associated with the two-component transformation and can be readily implemented into conventional quantum chemistry programs. TIC was verified through numerical calculations using the second- and third-order unitarized Douglas–Kroll method, which is newly derived for the validation of TIC, and the infinite-order two-component method. The numerical validation results suggested that TIC could sufficiently reproduce the results of primitive basis sets for both atoms and molecules.

Theoretical interpretations of photoelectron spectra of platinum atom, its cation and anion

Results of theoretical research on the ground and excited states of the platinum atom, its Pt− anion, and Pt+ cation are presented. Calculations were carried out using the four-component multi-configuration Dirac-Hartree-Fock method with the spin-free relativistic eight-order Douglas-Kroll-Hess method, and the infinite order two-component method at high correlated level. The spin-orbit (SO) coupling is introduced via the restricted active space state interaction method with the use of the atomic mean field SO integrals. The results are interpreted in comparison with the experimental data. The theoretical analysis suggests different assignments and interpretations of some atomic and ionic states, and existence of three anionic bound states. The obtained electron affinity to Pt−5d96s22D5/2 ground state is 2.104 eV (experimental value is 2.125 eV) which can be considered as very accurate result. The photodetachment Pt−1 to Pt0 spectra is provided. A comparative analysis of the accuracy of two-component methods is also presented.

Theoretical interpretation of photoelectron spectra of the iridium neutral atom and anion

The results of theoretical calculations for the ground and excited levels of the iridium neutral atom and its negative ion are presented, and the corresponding photodetachment energies. Calculations were carried out with the four-component multiconfiguration Dirac-Hartree-Fock method and with the spin-free relativistic second- and eight-order Douglas-Kroll-Hess method, and the infinite order two-component method, and high-level correlated methods. The spin-orbit coupling is introduced via the restricted active space state interaction method with the use of the atomic mean-field SO integrals. The results are compared and interpreted in comparison with the experimental results. The theoretical analysis suggest different assignment and interpretation of atomic and anionic levels, and existence of several anionic bound states. A comparative analysis of the accuracy of two-component methods is also presented.

Implementation of Picture Change Corrected Density Functional Theory Based on Infinite-Order Two-Component Method to GAMESS Program

Implementation of Picture Change Corrected Density Functional Theory Based on Infinite-Order Two-Component Method to GAMESS Program

Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory.

In contrast to nonrelativistic density functional theory, the ratio between the von Weizsäcker and the Kohn-Sham kinetic energy density, commonly used as iso-orbital indicator t within exchange-correlation functionals beyond the generalized-gradient level, violates the exact iso-orbital limit and the appropriate parameter range, 0 ≤ t ≤ 1, in relativistic density functional theory. Based on the exact decoupling procedure within the infinite-order two-component method and the Cauchy-Schwarz inequality, we present corrections to the relativistic and the picture-change-transformed nonrelativistic kinetic energy density that restores these exact constraints. We discuss the origin of the new correction terms and illustrate the effectiveness of the current approach for several representative cases. The proposed generalized iso-orbital indicator tλ is expected to be a useful ingredient for the development of relativistic exchange-correlation functionals.

Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method.

We present an efficient implementation of relativistic exact exchange within the infinite-order two-component method (IOTC) by employing a state-of-the-art seminumerical integration technique. For accurate consideration of the picture change, inherent to two-component methods, we propose a new scheme based on a relativistic or picture-change transformation of the density matrix, which provides a simple and efficient formulation of relativistically transformed quantities such as the electron density or exact exchange and thus avoids expensive integral transformations. We show that the new scheme does not introduce additional numerical or theoretical errors beyond the approximations of the IOTC method. For the efficient implementation of exact-exchange integrals, we build upon a modified version of the chain-of-spheres exact-exchange (COSX) method. In addition to the conventional overlap and density matrix screening by S- and P-junctions, respectively, we introduce a new simple screening technique in the sense of the original COSX method by additionally considering the asymptotic decay of the integrals over the Coulomb operator within the new F-junctions. Together with the picture-change transformation of the density matrix, this modified COSX method is shown to provide superior efficiency for the calculation of relativistic exact exchange compared to a conventional analytical direct self-consistent-field implementation of exact exchange.

Relativistic calculations of X-ray photoelectron spectra and the accuracy of the IOTC method*

In this paper, the authors have applied the infinite-order two-component (IOTC) method to study the X-ray spectra of noble gases. The effect of spin–orbit coupling is introduced via the restricted active space interaction (RASSI) method with the use of the atomic mean-field AMFI integrals. For the deep core energies the discrepancies between the experimental and calculated values can be still quite large. To explain these differences the quantum electrodynamic corrections have been calculated such as Breit energy, self-energy and vacuum polarisation. The comparison between results of the IOTC method and the Douglas–Kroll–Hess (DKHn) approximation has been presented as well.

Relativistic study of tautomerism and core electron binding energies of thio- and selenocytosine

We applied the spin-free relativistic infinite-order two-component method to calculate the core-electron binding energies of different tautomeric structures of thio- and selenocytosine. The importance of relativistic effects in the ionization of 1s electrons was studied for selenocytosine. The present method provides a reasonably simple and reliable computational tool for calculating the core electron binding energies of molecules containing heavy atoms. The method can also be used for characterization of different tautomeric structures of nucleic acid basis.

The quadrupole moment of the As nucleus from molecular microwave data and calculated relativistic electric field gradients

The ‘molecular’ value of the nuclear quadrupole moment of the 75As nucleus is determined combining the experimental data for quadrupole coupling constant and the calculated electric field gradient in the AsP molecule. The accurate calculations have been carried out at the CCSD(T) level. The relativistic effects were accounted for using the infinite-order two-component method in the scalar approximation. The new recommended value of the nuclear quadrupole moment of 75As obtained in this work is 311(2) mb and is more precise than the previous ‘muonic’ value.

Relativistic two-component infinite order method for atomic core ionization potentials

In this paper the authors have applied the infinite-order two-component method (IOTC) to compute the valence and inner shell ionization potentials for the Ne, Ar, Kr, and Xe elements. The obtained results show the very good performance of the recently defined relativistic IOTC method. They also confirm the importance of the relativistic effects in the determination of the inner shell ionization potentials.

Convergence of approximate two-component Hamiltonians: How far is the Dirac limit

A systematic elimination of the off-diagonal parts of the Dirac Hamiltonian is carried out in the spirit of the Douglas-Kroll [Ann. Phys. 82, 87 1974] approach and the recently proposed infinite-order two-component method. The present approach leads to a series of approximate two-component Hamiltonians which are exact through a certain order in the external potential. These Hamiltonians are used to study the convergence pattern of approximate two-component theories. It is shown that to achieve an acceptably high accuracy for low-lying one-electron levels in heavy and superheavy systems one needs to use approximate Hamiltonians of prohibitively high order in the external potential. One can conclude that the finite-order two-component Hamiltonians are of limited usefulness in accurate relativistic calculations for heavy and superheavy systems.