Symmetry-adapted-cluster Configuration-interaction general-R Research Articles

Geometric, electronic and spectral properties of germanium and Eu-doped germanium clusters

This study explored the geometric, electronic, and spectral properties of germanium and Eu-doped germanium clusters and compared their simulated PES spectra. The stability of Gen and EuGen nanoclusters was examined with density functional theory using FHI-aims as a software package. Symmetry-adapted cluster-configuration interaction general-R (SAC-CI-General-R) method and the SDD basis set were adopted to determine ionization energies and calculate their intensities. Natural bond orbital (NBO) calculations were performed to determine the effective molecular orbitals in the ionization and study the electron density on the nanoclusters. The shape of molecular orbitals (MO) involved in the ionization process for each structure was displayed and interpreted. The analyses of binding energies showed that increasing the size of nanoclusters leads to more stability for nanoclusters. Ionization energy and the photoelectron spectrum of these clusters indicated that Eu as an impurity reduces ionization energy and shifts the ionization processes towards infrared wavelengths. Interestingly, pure and doped clusters followed a similar pattern in terms of an increase/decrease in the first ionization energy compared to n-1 and n + 1 clusters.

Structural and electronic properties of Gen and EuGen-1 nanoclusters: A full potential DFT study

In this work, the stability, structure and electronic properties of the nanoclusters of germanium (Gen) and europium atom doped germanium clusters (EuGen-1) with n=2 to 12, 15 and 20 were investigated. First, the stability of nanoclusters such as Gen and EuGen-1 was addressed using FHI-aims as a software package based on the density functional theory. Then the lowest-energy structures were selected for calculating the first vertical ionization with the symmetry adapted cluster-configuration interaction General-R (SAC-CI-General-R) method. The results of this research show that there is a good agreement between calculation and experiment ionization potential for Gen nanoclusters. Generally, the analyses of binding energies show that increasing the size of nanoclusters leads to more stability for nanoclusters. The most stable nanoclusters for EuGen can be created with exchanging the Eu atom in the most stable Gen+1 nanoclusters, but there is an exception for n=11 case. Here, the second difference in energy (∆2E) and gap energy are computed for the stable nanoclusters. The results of ionization energy and second difference in energy confirm that Ge7 and Ge10 also EuGe8 and EuGe10 have the most stability.

Calculation of Dyson orbitals using a symmetry-adapted-cluster configuration-interaction method for electron momentum spectroscopy:N2andH2O

The symmetry-adapted-cluster (SAC) configuration-interaction (CI) theory was introduced to interpret the non-coplanar symmetric ($e$,$2e$) results. Dyson orbitals derived from the bench-marked SAC CI general-R method were utilized for computing the electron momentum distributions. The corresponding excitation energies and spectroscopic factors can be used to reproduce the ionization spectra. The implementation was demonstrated by examples of ${\mathrm{N}}_{2}$ and ${\mathrm{H}}_{2}$O. The electron momentum distributions calculated using SAC CI method were compared with recent experimental results, as well as the Hartree-Fock and density-functional-theory calculations. The SAC CI method gave the best performance on the description of the experimental momentum distributions. It was found that the electron momentum distributions of Dyson orbitals related to the satellite lines can be notably different from those of their parent orbitals due to the electron correlation in the initial target states. Present work demonstrated that the SAC CI theory is a very useful and accurate tool for interpreting high-resolution electron momentum spectroscopy results.

Dyson orbitals of N2O: Electron momentum spectroscopy and symmetry adapted cluster-configuration interaction calculations

Electron momentum spectroscopy and symmetry adapted cluster-configuration interaction (SAC-CI) theory were combined to study electron correlation effects in nitrous oxide molecule (N(2)O). The SAC-CI General-R method accurately reproduced the experimental ionization spectrum. This bench-marked method was also introduced for calculating the momentum distributions of N(2)O Dyson orbitals. Several calculated momentum distributions with different theoretical methods were compared with the high resolution experimental results. In the outer-valence region, Hartree-Fock (HF), density functional theory (DFT), and SAC-CI theory can well describe the experimental momentum distributions. SAC-CI presented a best performance among them. In the inner-valence region, HF and DFT cannot work well due to the severe breaking of the molecular orbital picture, while SAC-CI still produced an excellent description of experimental momentum profiles because it can accurately take into account electron correlations. Moreover, the thermally averaged calculation showed that the geometrical changes induced by the vibration at room temperature have no noticeable effects on momentum distribution of valence orbitals of N(2)O.

Ab initio calculations of the ionization spectrum of SO2

The ionization spectrum of sulfur dioxide has been successfully studied by using the symmetry-adapted-cluster configuration-interaction (SAC-CI) general-R and SD-R methods and the basis set correlation-consistent polarized valence triple-zeta (cc-pVTZ). The SAC-CI general-R method reproduces the experimental spectrum well for both the main peaks and the satellite peaks of ionization spectrum of SO2. The sequence of ionic states corresponding to main peaks of SO2 has been re-determined according to the SAC-CI conclusions and it is reordered as X̄2A1, Ã2B2, B̄2A2, C̄2B1, D̄2A1, Ē2B2 and F̄2A1. Besides, the equilibrium structures and adiabatic ionization potentials (AIPs) of ionic states of main peaks of SO2 are calculated by using the SAC-CI SD-R method.

Relativistic effects in K-shell ionizations: SAC-CI general-R study based on the DK2 Hamiltonian

Relativistic effects in K-shell ionizations were studied using the symmetry adapted cluster-configuration interaction (SAC-CI) general-R method based on the spin-free part of the second-order Douglass–Kroll–Hess (DK2) Hamiltonian. The core–electron binding energies (CEBEs) of F, Si, P, S, and Cl atoms of several molecules were calculated. The relativistic effect in the CEBEs of the second-row atoms was 4–9eV. The relativistic effect was mostly overestimated by the Koopmans’ theorem and was reduced to the extent of 0.15–0.4eV by including the orbital relaxation and electron correlations. The present method provides a simple and reliable computational tool for calculating the CEBEs of molecules containing heavy elements.

Singly and doubly excited states of butadiene, acrolein, and glyoxal: Geometries and electronic spectra

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 A and 0.7 degrees for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 (1)A(g) states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states.

Theoretical Fine Spectroscopy with SAC-CI Method: Outer- and Inner-Valence Ionization Spectra of CO and N2

Outer- and inner-valence ionization spectra of CO and N2 were studied by the SAC-CI (symmetry-adapted-cluster configuration-interaction) general-R method. Fine details of experimental spectra of these molecules were reproduced and quantitative assignments of the peaks were proposed. Both outer- and inner-valence satellites were classified into the shake-up states including the valence or Rydberg excitations. For CO, theoretical satellite spectrum up to 50 eV was presented and the nine bands of 22-50 eV observed by EMS and eight bands of 22-34 eV by XPS (C-K) were characterized in detail. Numerous satellite peaks with distributed intensity were obtained and some of them, especially for bands 4, 5, 6 and 7, were predominantly described by triple-electron processes. For N2, the spectrum up to 45 eV was calculated and the complex satellite peaks observed by XPS in the lower energy region 20-33 eV were interpreted. The detailed assignments for the (2σg-1) satellite states in the higher-energy region 33-45 eV were also presented.

Theoretical fine spectroscopy with symmetry adapted cluster–configuration interaction general-R method: First-row K-shell ionizations and their satellites

Molecular core ionization spectra and their satellites were studied by the symmetry adapted cluster-configuration interaction (SAC-CI) general-R method. The core-electron binding energies of C, N, O, and F atoms of 22 molecules were calculated with an average deviation of 0.11 eV from the experimental values. The energy splittings between K-shell gerade and ungerade states were calculated and discussed in relation to the bond length. The satellite spectra of the C 1s and N 1s core ionizations of methane and ammonia were investigated. The SAC-CI general-R method gave many shake-up states with moderate intensities, reproducing the general feature of the experimental spectra, and thus enabling the detailed understanding and assignments of the core-electron ionization spectra.

Fine Theoretical Spectroscopy Using SAC-CI General-R Method: Outer- and Inner-Valence Ionization Spectra of N2O and HN3

Abstract Fine theoretical spectroscopy for the outer- and inner-valence ionization spectra has been presented by using the SAC-CI (symmetry adapted cluster-configuration interaction) general-R method applied to N2O and HN3. The SAC-CI general-R method accurately simulated the experimental spectra and the detailed assignments of the satellite peaks were proposed. The continuous peaks I ∼ V of N2O observed by the dipole (e,2e) spectroscopy were finely reproduced. In particular, the low-lying satellites were calculated in good agreement with the experiment; two 2Π shake-up states at the foot of the C state, 2Σ and 2Π states for the peak I. For HN3, new interpretation was proposed for the outer-valence region, namely, peaks 3 ∼ 5 are composed of the mixture of the single-electron main peaks and the two-electron shake-up peaks. Inner-valence ionization spectrum of HN3 was theoretically predicted for which no experimental spectrum has been reported.

Fine theoretical spectroscopy using symmetry adapted cluster-configuration interaction general-R method: Outer- and inner-valence ionization spectra of CS2 and OCS

Fine theoretical spectroscopy has been presented by the SAC-CI (symmetry adapted cluster-configuration interaction) general-R method for the outer- and inner-valence ionization spectra of CS2 and OCS. The SAC-CI general-R method simulated the experimental spectra quite accurately and the detailed assignments of the satellite peaks were given. For CS2, four outer-valence satellites Πu2 states were calculated, one of which was attributed to the recently observed peak (1′). Numerous Σu+2 and Σg+2 satellite peaks were obtained in the inner-valence region and some of them were dominantly described by triple electron processes; the quadruple R-operators were found to be important for describing these states in the general-R method. For OCS, the relative position of the main peaks was correctly reproduced and the higher R-operators were found to be important for the ordering of A and B states. In the energy region of 24–36 eV, continuous spectra of numerous Σ+2 satellites were obtained, which reproduced the feature of the photoelectron spectrum.

Theoretical study on the outer- and inner-valence ionization spectra of H2O, H2S and H2Se using the SAC-CI general-R method

The outer- and inner-valence ionization spectra of the Group VI hydrides H2O, H2S and H2Se below the double-ionization threshold were studied by the SAC-CI (symmetry-adapted-cluster configuration-interaction) general-R method. The SAC-CI method quite accurately reproduced the experimental spectra of these hydrides and gave detailed characterizations of the shake-up states. Several unknown satellite peaks were predicted. The shake-up state which includes excitations to the Rydberg orbitals was found to be very important for describing the satellite peaks of these hydrides. A detailed inner-valence satellite spectrum of H2Se is theoretically proposed prior to any experimental observation.

Electronic excitation and ionization spectra of azabenzenes: Pyridine revisited by the symmetry-adapted cluster configuration interaction method

Electronic excited and ionized states of pyridine were reinvestigated by the symmetry-adapted cluster configuration interaction (SAC-CI) method using an extended basis set and a wide active space. The present SAC-CI results for the singlet and triplet excited states are greatly improved and agree well with the experimental observations, providing a firm assignment of all low-lying n→π* and π→π* valence excited states observed in the vacuum ultraviolet spectrum and electron energy-loss spectrum. The ionization potentials were reexamined by the SAC-CI general-R (R represents excitation operator) method. The first four ionization potentials are greatly improved compared with our previous results obtained by the SAC-CI single- and double-R (SD-R) method. The present theoretical ionization potentials are in good agreement with the experimental values in high-resolution synchrotron photoelectron spectrum for energy regions up to 25 eV (which contain outer- and inner-valence regions), and give a detailed theoretical assignment for the photoelectron spectra.

Electronic excitation and ionization spectra of cyclopentadiene: Revisit by the symmetry-adapted cluster–configuration interaction method

Electronic excitation and ionization spectra of cyclopentadiene (CP) were reinvestigated by the symmetry-adapted cluster (SAC) and SAC–configuration interaction (SAC-CI) method with an extended basis set and a wide active orbital space. To give a satisfactory interpretation of the general profile of the observed excitation spectrum, 40 low-lying excited singlet and triplet states (with excitation energies of up to 9.5 eV) were computed. The calculated excitation energies were greatly improved compared to those reported previously. All of the peaks in the experimental spectrum were reassigned theoretically with small deviations. The natures of the low-lying valence and Rydberg-excited states were discussed in detail, and the results were also compared with those of some other recent theoretical studies. The ionization energies calculated by the SAC-CI general-R method agree well with the experimental peaks in the photoelectron spectrum. A number of two-electron shake-up states were calculated below 23 eV.

Outer- and inner-valence ionization spectra of N 2 and CO: : SAC-CI (general-R) compared with full-CI spectra

The SAC-CI (symmetry-adapted-cluster configuration-interaction) (general-R) method describes the ionization and shake-up spectra of N 2 and CO in almost complete agreement with the full-CI results, though the computational labour of the former is much smaller that that of the latter. The SAC-CI (general-R) method is accurate for both valence and inner-valence regions of ionization spectra, while the SAC-CI (SD-R) method is good for the outer-valence region, but not always so for the shake-up region.