Calculation Of Wave Functions Research Articles

Electron-impact excitations of highly charged tungsten ions and polarization study of their successive photon decay

Fully relativistic distorted wave theory has been utilized to study the electron-impact excitation of highly charged tungsten ions viz. Y-like (W35+), Sr-like (W36+), Rb-like (W37+) and Br-like (W39+). Electric dipole transitions pertaining to n = 4 → n′ = 4 states have been considered in these four ions. The electron excitation cross-sections are calculated for these ions in the wide range of electron-impact energies from excitation threshold to 20 keV. The required relativistic bound states wave functions for the initial and excited states of the ions are obtained using GRASP2k code. The accuracy of the computed wave functions is ascertained by comparing the calculated energies and oscillator strengths for the considered transitions with the available theoretical and experimental results. For the direct application of the cross-sections to the plasma modelling our calculated cross-sections are fitted to suitable analytical expressions. Further, the degree of linear polarization of the emitted photons due to the decay of the electron from the excited tungsten ions to their respective ground states is also calculated using density matrix theory. There are no previous calculations available for the cross-sections and polarizations to compare with our results of these ions.

RASPT2 study of the valence excited states of an iron-porphyrin-carbonyl model complex.

Multireference wavefunction calculations of the singlet valence excited states of an iron-porphyrin-pyrazine-carbonyl complex up to the Soret band (about 3 eV) are presented. This complex is chosen to be a model for the active site of carboxyhemoglobin/carboxymyoglobin. The investigations are performed at the restricted active space second-order perturbation (RASPT2) level involving an extended active space on the porphyrin ligand in addition to the active orbitals needed for the description of the metal-ligand interactions. Metal-to-ligand-charge-transfer states d → π* and some metal-centered d → d transitions are found in the lowest part of the spectrum, below the first π → π* intraporphyrin transitions (Q band). Doubly excited states involving simultaneous intraporphyrin and metal-centered excitations are found in the vicinity of the second set of intraporphyrin transitions (the so-called Soret band). The effect of the extension of the active space on the porphyrin ligand beyond the Gouterman's orbitals set is investigated together with the effect of inclusion of the ionization potential electron affinity shift in the RASPT2 treatment. © 2019 Wiley Periodicals, Inc.

Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density.

We introduce an approximation to the short-range correlation energy functional with multideterminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, the density gradient, and the on-top pair density, which locally interpolates between the standard Perdew-Burke-Ernzerhof correlation functional at a vanishing range-separation parameter and the known exact asymptotic expansion at a large range-separation parameter. When combined with (selected) configuration-interaction calculations for the long-range wave function, this approximation gives accurate dissociation energy curves of the H2, Li2, and Be2 molecules and thus appears as a promising way to accurately account for static correlation in range-separated density-functional theory.

Molecular and Electronic Structure, and Hydrolytic Reactivity of a Samarium(II) Crown Ether Complex.

The reaction of SmI2 with dibenzo-30-crown-10 (DB30C10), followed by metathesis with [Bu4N][BPh4], allows for the isolation of [SmII(DB30C10)][BPh4]2 as bright-red crystals in good yield. Exposure of [Sm(DB30C10)]2+ to solvents containing trace water results in the conversion to the dinuclear SmIII complex, Sm2(DB30C10)(OH)2I4. Structural analysis of both complexes shows substantial rearrangement of the crown ether from a folded, Pac-Man form with SmII to a twisted conformation with SmIII. The optical properties of [SmII(DB30C10)][BPh4]2 exhibit a strong temperature dependence and change from broad-band absorption features indicative of domination by 5d states to fine features characteristic of 4f → 4f transitions at low temperatures. Examination of the electronic structure of these complexes via ab initio wave function calculations (SO-CASSCF) shows that the ground state of SmII in [SmII(DB30C10)]2+ is a 4f6 state with low-lying 4f55d1 states, where the latter states have been lowered in energy by ∼12 000 cm-1 with respect to the free ion. The decacoordination of the SmII cation by the crown ether is responsible for this alteration in the energies of the excited state and demonstrates the ability to tune the electronic structure of SmII.

Radiative and Auger transitions of K-shell excited resonance states in boron-like sulfur ion

<sec>Non-relativistic energy values and wave functions of the K-shell excited resonance states 1s2s<sup>2</sup>2p<sup>2</sup>, 1s2s2p<sup>3</sup>, 1s2p<sup>4 2, 4</sup><i>L</i> (<i>L</i> = S, P, D) in boron-like sulfur ion are calculated in the frame of multi-configuration saddle-point variation method. The electron correlation effects are considered by the expansion of configuration wave function. The wave functions are constructed and optimized by the orbital-spin angular momentum partial waves selected based on the rule of configuration interaction. To saturate the wave functional space and to improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Then, the mass polarization effect and relativistic correction are calculated by the perturbation theory. The quantum electrodynamics (QED) effect and higher-order relativistic correction are considered by the screened hydrogenic formula. Furthermore, the energy shift originating from the interaction between closed channel and open channel is also calculated. Finally, the accurate relativistic energy levels for these resonance states are obtained by adding the non-relativistic energy and all corrections.</sec><sec>Using the optimized wave functions, the line strengths, oscillator strengths, radiative transition rates and transition wavelengths of electric-dipole transitions for the K-shell excited resonance states in boron-like sulfur ion are systematically calculated. In this work, the oscillator strengths and transition rates are given in the length, velocity, and acceleration gauges. The good agreement among the three gauges reflects that the calculated wave functions are reasonably accurate. The calculated radiative transition rates and transition wavelengths are compared with other theoretical data. Good agreement is obtained except the transition: 1s2s(<sup>3</sup>S)2p<sup>3</sup> <sup>2</sup>P<sup>o</sup>→1s2<sup>2</sup>s2p<sup>2 2</sup>D. The deviation between our theoretical result and the MCDF theoretical value is about 46%, which needs further verifying. The Auger rates, Auger branching ratios, and Auger electron energy values of the important decay channels of the K-shell excited states are calculated by the saddle-point complex-rotation method. The calculated Auger rates and Auger electron energy values are also in good agreement with the corresponding reference data. For some K-shell states, the related energy levels and Auger branching ratios are reported for the first time. The present calculations results will provide valuable theoretical data for the calibration of spectral lines and Auger electron spectra in the relevant experiments.</sec>

Subspace Density Matrix Functional Embedding Theory: Theory, Implementation, and Applications to Molecular Systems.

We introduce the subspace density matrix functional embedding theory (sDMFET), in which optimization of the nonlocal embedding potential and subsequent embedded correlated wave function calculations are carried out within a truncated subspace determined by a Schmidt decomposition. As compared to the original density matrix functional embedding theory [K. Yu and E. A. Carter, Proceedings of the National Academy of Sciences 2017 , 114 , E10861 ], the computational cost of sDMFET is significantly reduced while the accuracy is preserved. We perform test calculations for both covalently and noncovalently bound molecular systems to demonstrate the feasibility of our theory.

Dependence of band structure and exciton properties of encapsulated WSe2 monolayers on the hBN-layer thickness

The optical properties of two-dimensional transition metal dichalcogenide monolayers such as MoS$_2$ or WSe$_2$ are dominated by excitons, Coulomb bound electron-hole pairs. Screening effects due the presence of hexagonal-BN surrounding layers have been investigated by solving the Bethe Salpeter Equation on top of GW wave functions in density functional theory calculations. We have calculated the dependence of both the quasi-particle gap and the binding energy of the neutral exciton ground state E$_b$ as a function of the hBN layer thickness. This study demonstrates that the effects of screening at this level of theory are more short-ranged that it is widely believed. The encapsulation of a WSe$_2$ monolayer by three sheets of hBN (around 1 nm) already yields a 20 % decrease of E$_b$ whereas the maximal reduction is 27% for thick hBN. We have performed similar calculations in the case of a WSe$_2$ monolayer deposited on stacked hBN layers. These results are compared to the recently proposed Quantum Electrostatic Heterostructure approach.

Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation.

The information contained within ground-state one- and two-electron reduced-density matrices (RDMs) can be used to compute wave functions and energies for electronically excited states through the extended random phase approximation (ERPA). The ERPA is an appealing framework for describing excitations out of states obtained via the variational optimization of the two-electron RDM (2-RDM), as the variational 2-RDM (v2RDM) approach itself can only be used to describe the lowest-energy state of a given spin symmetry. The utility of the ERPA for predicting near-edge features relevant to x-ray absorption spectroscopy is assessed for the case that the 2-RDM is obtained from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation. A class of killer conditions for the CASSCF-specific ERPA excitation operator is derived, and it is demonstrated that a reliable description of core-level excitations requires an excitation operator that fulfills these conditions; the core-valence separation (CVS) scheme yields such an operator. Absolute excitation energies evaluated within the CASSCF/CVS-ERPA framework are slightly more accurate than those obtained from the usual random phase approximation (RPA), but the CVS-ERPA is not more accurate than RPA for predicting the relative positions of near-edge features. Nonetheless, CVS-ERPA is established as a reasonable starting point for the treatment of core-level excitations using variationally optimized 2-RDMs.

Evaluating Density Functionals by Examining Molecular Structures, Chemical Bonding, and Relative Energies of Mononuclear Ru-Cl-H-PR3 Isomers.

In order to define a robust level of theory using density functionals for investigating the reactivity of ruthenium complexes, we used benchmark wave function theory, with saturated basis sets to validate generalized gradient approximation (GGA), meta-GGA, and hyper-GGA functionals in the presence and absence of empirical dispersion and range-separated corrections. We first selected potentially suitable functionals that gave accurate predictions of the relative energetics of coordination isomers. These functionals were further evaluated for the chemical accuracy of their predicted geometric and electronic structures. For the latter, both the ionic and covalent interactions were considered. The reference level of theory for comparison was coupled-cluster perturbation theory using full treatment of singles and doubles (CCSD) with a saturated triple-ζ quality basis set (TZVP) and corresponding small-core, effective core potentials for ruthenium. Several population analysis methods were evaluated to predict the ionic interactions. We found that the atomic charges obtained from fitting the electrostatic potential provided the most reasonable estimates for the ruthenium complexes. The covalent interactions were quantified by considering the atomic compositions of Ru 4d x2- y2- and 4d z2-based frontier unoccupied orbitals. Comparison of more than two dozen functionals with reference data from high-level wave function calculations revealed trends that allowed for the formulation of an optimal hybrid density functional: PBE exchange and correlation functionals with 50% HF exchange component. This level of theory was found to reproduce the experimental structure of Ru(II) complexes. These complexes were used to investigate chemical speciation in a simplified model for an ionic liquid environment.

Calculating bound states resonances and scattering amplitudes for arbitrary 1D potentials with piecewise parabolas

Even for one-dimensional (1D) potentials, the calculation of highly excited bound states and resonances (in particular broad and overlapping ones) often requires heavy numerical tools. The method presented here is based on representing an arbitrary 1D potential as a set of piecewise parabolas, where the solutions of the Schrödinger equation within each parabolic region are analytic. Outgoing, incoming, or zero-valued boundary conditions are imposed to solve for bound and resonance states, while asymmetric boundary conditions are enforced to calculate scattering amplitudes. The developed method is also applicable for complex potentials, as for example found in non-Hermitian symmetric systems (such as optical waveguides, where the spectrum varies from real to complex as a function of gain and loss). We demonstrate for several model Hamiltonians that calculations of energies, decay rates, scattering amplitudes, and wave functions are obtained in high accuracy and with minimal computational effort in comparison to other widely used methods. We believe our approach will be useful in many areas of physics and chemistry, and for example can be used to calculate various types of resonances, to solve scattering problems in cold molecular collisions, and to create analytical basis functions for multidimensional potentials.

Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes.

Relativistic multireference ab initio wave function calculations within the restricted active space (RAS) framework were performed to calculate metal and ligand X-ray absorption (XAS) near-edge spectroscopy (XANES) intensities for the metal M4,5 edges of [PuO2(H2O)5]2+, [AnVIO2]2+ (An = U, Np, Pu), and [AmCl6]3- and the Cl K edge of the Am complex. The extent of An(5f)-ligand bonding was determined via natural localized molecular orbital analyses of the relevant spin-orbit coupled multireference states. The calculated spectra are in good agreement with experiments and allow a detailed assignment of the observed spectral features. The XANES M4,5-edge spectra are representative of the actinide orbital covalency in the probed core-excited states, which may be different from the ground-state covalency. An assignment of ground-state An orbital covalency based on XAS spectra should therefore be made with caution.

Non-Relativistic Limit of Neutron Beta-Decay Cross-Section in the Presence of Strong Magnetic Field

One of the most important reactions of the URCA that lead to the cooling of a neutron star, is neutron beta-decay ( ). In this research, the energy spectra and wave functions of massive fermions taking into account the Anomalous Magnetic Moment (AMM) in the presence of a strong changed magnetic field are calculated. For this purpose, the Dirac-Pauli equation for charged and neutral fermions is solved by Perturbation and Frobenius series method, respectively. The results of the Frobenius series method are in good agreement with the results of Nikiforov-Uvarov method (NU). In continuous, using the calculated wave functions, the general relation of neutron decay cross-section in the non-relativistic limit has been obtained. This relation has been derived by the four-fermion Lagrangian within the framework of the standard model of weak interactions. These calculations from the perspective of nuclear astrophysics can be important.

Analytical Nuclear Excited-State Gradients for the Second-Order Approximate Coupled-Cluster Singles and Doubles (CC2) Method Employing Uncoupled Frozen-Density Embedding.

We report the derivation and implementation of analytical orbital-relaxed properties and nuclear gradients for excited states using the second-order approximate coupled-cluster singles and doubles (CC2) model combined with uncoupled frozen-density embedding (FDEu). An implementation of the algebraic diagrammatic construction through second-order ADC(2), which arises from simplification of RICC2 FDEu, is also presented. In order to ensure a RICC2 FDEu Lagrange functional that is linear in the Lagrange multipliers, the Hartree-Fock density is employed for the target subsystem in the embedding contributions. The accuracy of the new scheme is assessed using the carbon monoxide molecule, 4-aminophthalimide, and a benzonitrile dimer, revealing that the obtained errors are below the method error of RICC2. Using density functional theory for the environment, the efficiency of the new method is illustrated by computing the perturbed excited-state dipole moment of a chromophore in a biological environment. For this system, comprising 32 molecules consisting of 366 atoms in total, the computation requires only a couple of days on a standard compute node. RICC2 FDEu thus enables large-scale calculations of ab initio wave functions for molecules in complex environments as routine applications.

A Pseudotetrahedral Uranium(V) Complex.

A series of uranium amides were synthesized from N, N, N-cyclohexyl(trimethylsilyl)lithium amide [Li][N(TMS)Cy] and uranium tetrachloride to give U(NCySiMe3) x(Cl)4- x, where x = 2, 3, or 4. The diamide was isolated as a bimetallic, bridging lithium chloride adduct ((UCl2(NCyTMS)2)2-LiCl(THF)2), and the tris(amide) was isolated as the lithium chloride adduct of the monometallic species (UCl(NCyTMS)3-LiCl(THF)2). The tetraamide complex was isolated as the four-coordinate pseudotetrahedron. Cyclic voltammetry revealed an easily accessible reversible oxidation wave, and upon chemical oxidation, the UV amido cation was isolated in near-quantitative yields. The synthesis of this family of compounds allows a direct comparison of the electronic structure and properties of isostructural UIV and UV tetraamide complexes. Spectroscopic investigations consisting of UV-vis, NIR, MCD, EPR, and U L3-edge XANES, along with density functional and wave function calculations, of the four-coordinate UIV and UV complexes have been used to understand the electronic structure of these pseudotetrahedral complexes.

Atomic-pair theorem for universal matrix representatives of molecules and atomic clusters in non-relativistic Born-Oppenheimer approximation

The mathematical underpinnings of a universal atomic-pair based approach to ab initio calculations of the electronic wave functions and energies of molecules and other atomic clusters are reported in non-relativistic Born-Oppenheimer approximation. The general approach utilizes the closure of an orthonormal (Eisenschitz-London) outer product of atomic spectral eigenstates to support totally antisymmetric aggregate eigenstates in the absence of explicit term-by-term atomic-product basis antisymmetry. Meaningful definitions of atomic-pair interaction operators and of their corresponding universal matrix representatives on the atomic product basis are obtained in this way for calculations on physical and chemical aggregates. Symmetric-group-based permutation-symmetry methods for partitioning of aggregate Hamlitonian matrices, performed to date by unitary transformations to remove unphysical “non-Pauli” states after aggregate Hamiltonian matrix construction, are supplemented here with a new two-step procedure. The new approach, which combines explicit antisymmetrization of atomic pair matrices with unitary transformation of aggregate Hamiltonian matrices, is described here in complete mathematical detail. Conditions are established from the new development under which enforcement of pairwise-atomic antisymmetry alone can be sufficient for calculations of electronic energies, providing an efficient approach for practical applications, as well as long-absent theoretical support for related semi-empirical and ad hoc methods widely employed in computational molecular physics and quantum chemistry. An exact expression is obtained for total electronic energies from the solution of the Schrödinger equation in the universal form of sums over pairwise-atomic interaction energies uniquely defined within a molecule in the absence of subjective additional conditions. Wigner rotation matrices are employed to orient pairs of interacting atoms within an aggregate in the implementation of the approach, requiring calculations of the universal pair interaction matrices as functions of radial separations only. Such information can be obtained once and for all from molecular diatomic calculations and retained for subsequent use, avoiding repeated evaluations of the electronic integrals commonly required in conventional variational determinations of accurate potential energy surfaces. Diagonalizations of large Hamiltonian matrices are avoided in favor of optical potential, Krylov-Lanczos, and previously described Stieltjes-Techebycheff methods in determination of aggregate Schrödinger eigenspectra.

Low-Spin Fe(III) Macrocyclic Complexes of Imidazole-Appended 1,4,7-Triazacyclononane as Paramagnetic Probes.

Two macrocyclic complexes of 1,4,7-triazacyclononane (TACN), one with N-methyl imidazole pendants, [Fe(Mim)]3+, and one with unsubstituted NH imidazole pendants, [Fe(Tim)]3+, were prepared with a view toward biomedical imaging applications. These low-spin Fe3+ complexes produce moderately paramagnetically shifted and relatively sharp 1H NMR resonances for paraSHIFT and paraCEST applications. The [Fe(Tim)]3+ complex undergoes pH-dependent changes in NMR spectra in solution that are consistent with the consecutive deprotonation of all three imidazole pendant groups at high pH values. N-Methylation of the imidazole pendants in [Fe(Mim)]3+ produces a complex that dissociates more readily at high pH in comparison to [Fe(Tim)]3+, which contains ionizable donor groups. Cyclic voltammetry studies show that the redox potential of [Fe(Mim)]3+ is invariant with pH ( E1/2 = 328 ± 3 mV vs NHE) between pH 3.2 and 8.4, unlike the Fe(III) complex of Tim which shows a 590 mV change in redox potential over the pH range of 3.3-12.8. Magnetic susceptibility studies in solution give magnetic moments of 0.91-1.3 cm3 K mol-1 (μeff value = 2.7-3.2) for both complexes. Solid-state measurements show that the susceptibility is consistent with a S = 1/2 state over the temperature range of 0 to 300 K, with no crossover to a high-spin state under these conditions. The crystal structure of [Fe(Mim)](OTf)3 shows a six-coordinate all-nitrogen bound Fe(III) in a distorted octahedral environment. Relativistic ab initio wave function and density functional theory (DFT) calculations on [Fe(Mim)]3+, some with spin orbit coupling, were used to predict the ground spin state. Relative energies of the doublet, quartet, and sextet spin states were consistent with the doublet S = 1/2 state being the lowest in energy and suggested that excited states with higher spin multiplicities are not thermally accessible. Calculations were consistent with the magnetic susceptibility determined in the solid state.

Energy levels and transition probabilities from the Rayleigh-Ritz variation method: C I and O III

The atomic parameters – energy levels, oscillator strengths, transition probabilities, and transition wavelengths have been presented for electric dipole transitions in C I and O III. The results include center-of-gravity energies of LS-terms of configurations 2s22p2, 2s22p3p for even parity and 2s2p3, 2s22p3s, 2s22p3d for odd parity, and probabilities of the corresponding important electric dipole transitions. The calculations are carried out using the multi-configuration Rayleigh-Ritz variation method with moderate-scale wavefunctions. The oscillator strength values in length and velocity gauges show fair agreement with each other, which indicates that the calculated wave functions are reasonably accurate. The calculated results are compared with existing experimental data. The present values show good agreement with the experimental data. The present transition probabilities should be useful for diagnostics as well as for precise spectral modeling in astrophysical and laboratory plasmas.

Elastic waves with correlated directional and orbital angular momentum degrees of freedom

We introduce a formalism that enables the calculation of elastic wave functions supported by parallel arrays of coupled one-dimensional elastic waveguides. These wave functions are expressed as tensor products of a spinor part associated with directional degrees of freedom and an orbital angular momentum (OAM) part associated with the phase of the coupled waveguides. We demonstrate that one can construct wave functions as a superposition of these elastic waves, which cannot be written as a tensor product of a spinor part and an OAM part. These elastic wave functions are not separable in the tensor product Hilbert space of directional and OAM subspaces. We show that we can construct maximally nonseparable states that are similar to Bell states.

Dissociative Chemisorption of O2 on Al(111): Dynamics on a Correlated Wave-Function-Based Potential Energy Surface.

Dissociative chemisorption of O2 on the Al(111) surface represents an extensively studied prototype for understanding the interaction between O2 and metal surfaces. It is well known that the experimentally observed activation barrier for O2 dissociation is not captured by conventional density functional theory. The interpretation of this barrier as a result of spin transitions along the reaction path has been challenged by recent embedded correlated wave function (ECW) calculations that naturally yield an adiabatic barrier. However, the ECW calculations have been limited to a static analysis of the reaction pathways and have not yet been tested by dynamics simulations. We present a global six-dimensional potential energy surface (PES) for this system parametrized with ECW data points. This new PES provides a reasonable description of the site-specific and orientation-dependent activation barriers. Quasi-classical trajectory calculations on this PES semiquantitatively reproduce both the observed translational energy dependence of the sticking probability and steric effects with aligned O2 molecules.

Квантовохимическое моделирование строения молекул иминодиуксусной кислоты и ее производных в водной среде

Проведены компьютерные вычисления атомного строения молекулы иминодиуксусной кислоты и ее гидратов в вакууме и водной среде. Показано, что учет диэлектрической проницаемости водной среды приводит к изменению длин ковалентных связей между атомами, валентных углов, эффективных зарядов и энергии связей. При этом топология химических связей изомера не изменяется. Присоединение одной молекулы воды приводит к смене позиции иона водорода, связанной с переносом его от иона кислорода к иону азота, что приводит к образованию цвиттер-структуры. Показано, присоединение молекулы воды к молекуле иминодиуксусной кислоты сопровождается возникновением трехцентровой ковалентной связи, что является физико-химическим механизмом термодинамической устойчивости цвиттер-структуры молекулы в водной среде.