CASSCF Research Articles

Halide Perovskite-Derived Compounds Rb2TeX6 (X = Cl, Br, and I): Electronic Structure of the Ground and First Excited States.

Herein, we report a study of the electronic structure of the ground and first excited states of Rb2TeCl6, Rb2TeBr6, and Rb2TeI6 halide-perovskite-derived crystals. Using X-ray photoelectron spectroscopy (XPS) measurements and density functional theory and multiconfiguration self-consistent field (MCSCF) calculations, the experimental and theoretical XPS spectra of the valence region were obtained. In addition, the effects of the cations and halogen atoms on the electronic structure were determined, and the classification of the excited states in double point group representation was carried out. Furthermore, a possible reason for the luminescence quenching in an isostructural series of crystals containing the [TeI6]2- anions was determined.

ISOTOPE SHIFT EFFECTS ON THE GROUND-STATE LEVELS FOR NEUTRAL TIN

Isotope shift effects including mass shift and field shift on the levels for the levels of 3P0,1,2, 1D2 and 1S0 for the ground-state configuration of the neutral tin (Sn I, Z= 50) have been investigated. In calculations, the multiconfiguration Hartree-Fock method within the frame work of Breit-Pauli Hamiltonian has been used. The calculation of isotope effects for tin has been here performed firstly although there are some works on the atomic structure of tin. The results including isotope shift effects on the levels have been discussed, and new energy values have been compared other available works in literature.

Experimental and theoretical results of resonant and normal Auger decay in dichloromethane

The Auger electron spectra after the chlorine 2p excitation and ionization in the gas phase CH2Cl2 and CD2Cl2 molecules were investigated both theoretically and experimentally. A series of high-level ab initio quantum mechanical calculations have been performed at multiconfigurational self-consistent field (MCSCF) and multireference configuration interaction (MRCI) levels of theory to compute the Cl L2,3VV Auger lines. Calculations were compared with the corresponding experimental photoexcited and photoionized spectra.

Synthesis of a Neutral Mononuclear Four-Coordinate Co(II) Complex Having Two Halved Phthalocyanine Ligands That Shows Slow Magnetic Relaxations under Zero Static Magnetic Field.

Syntheses of a novel pseudotetrahedral four-coordinate mononuclear Co(II) complex that has two halved phthalocyanine moieties as the ligands, [Co(half-Pc)2] (1), and its magnetic properties as a single molecule magnet (SMM) are reported. A one pot reaction of phthalonitrile and lithium methoxide followed by the coordination to a Co(II) ion gave 1 as an orange solid in a moderate yield. X-ray crystallography on 1 reveals tetragonally distorted coordination geometry around the Co(II) ion. The M- HT-1 plots suggest that 1 has large axial magnetic anisotropy. The ac magnetic susceptibility data of the magnetically diluted 1 (dil.1) clearly show that the complex acts as an SMM even in the absence of the external static magnetic field ( Hdc). The influence of intermolecular and intramolecular interactions for the magnetic relaxation behaviors has been discussed by comparison of the magnetic data of 1 and dil.1. The Orbach process is suggested as the predominant mechanism of magnetic relaxations in the high-temperature range, and the Arrhenius plots provide the effective relaxation energy barrier and pre-exponential factor of Ueff = 54.0 cm-1 and τ0 = 3.17 × 10-10 s, respectively. The direct estimation of the axial anisotropic parameter of 1 was successfully performed by high-field, multifrequency ESR measurements up to 55 T and 2.5 THz. The evaluated axial zero-field splitting (ZFS) energy of 57.0 cm-1 is comparable to the Ueff energy, confirming that the magnetic relaxations are initiated by the thermal excitation from the ground | M S⟩ = |±3/2⟩ states to the |±1/2⟩ states in the high-temperature range. The results of the ab initio calculations based on the CAS(7,5) SCF wave functions indicate that the ground states of 1 consist mainly of | M S⟩ = |±3/2⟩ states, while the first excited states are the mixture of | M S⟩ = |+1/2⟩ and |-1/2⟩.

The 13C nuclear magnetic shielding constants at the singlet excited states in CH2CCH2, CH2O, CH3CHO, CH3NH2, and CO

Abstract Quantum-chemical calculations of excited state nuclear shielding constants are reported for singlet states in CH2CCH2, CH2O, CH3CHO, CH3NH2, and CO. The multiconfigurational self-consistent field method is used to account for static correlation in the excited states. With one exception, the molecules considered had larger shielding constants in their excited states than in their ground states. This tendency towards deshielding is rationalized using the sum-over-states expression for magnetic response.

Spin-Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods.

The spin-orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ nd] q ( q = 1-4 and 6-9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin-orbit couplings (SOC) using one-electron Breit-Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations-relativistic elimination of small components (RESC), third-order Douglas-Kroll-Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction-were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ nd]5, the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d] q configuration ( q = 2-4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d] q configuration ( q = 6-8), the energy lowering of all 4F7/2, 5D1, and 5D3 states due to the SOC effects is smaller than those of the other SM states. This difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

Photoionization of neutral iron from the ground and excited states

The B-spline R-matrix method is used to investigate the photoionization of neutral iron from the ground and excited states in the energy region from the ionization thresholds to 2 Ry. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and term-dependent orbitals is employed for an accurate representation of the initial states of Fe i and the target wave functions of Fe ii. The close-coupling expansion contains 261 LS states of Fe ii and includes all levels of the 3d64s,3d54s2,3d7,3d64p, and 3d54s4p configurations. Full inclusion of all terms from the principal configurations considerably changes both the low-energy resonance structure and the energy dependence of the background cross sections. Partial cross sections are analyzed in detail to clarify the most important scattering channels. Comparison with other calculations is used to place uncertainty bounds on our final photoionization cross sections and to assess the likely uncertainties in the existing data sets.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate.

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.

Multiconfigurational Self-Consistent Field Theory with Density Matrix Embedding: The Localized Active Space Self-Consistent Field Method.

Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by breaking large systems into smaller, coupled subsystems. However, we recently [ Pham et al. J. Chem. Theory Comput. 2018 , 14 , 1960 .] encountered evidence that the approximate single-determinantal bath picture inherent to DMET is sometimes problematic when the complete active space self-consistent field (CASSCF) is used as a solver and the method is applied to realistic models of strongly correlated molecules. Here, we show this problem can be defeated by generalizing DMET to use a multiconfigurational wave function as a bath without sacrificing practically attractive features of DMET, such as a second-quantization form of the embedded subsystem Hamiltonian, by dividing the active space into unentangled active subspaces each localized to one fragment. We introduce the term localized active space (LAS) to refer to this kind of wave function. The LAS bath wave function can be obtained by the DMET algorithm itself in a self-consistent manner, and we refer to this approach, introduced here for the first time, as the localized active space self-consistent field (LASSCF) method. LASSCF exploits a modified DMET algorithm, but it is a variational wave function method; it does not require DMET's ambiguous error function minimization, and it reproduces full-molecule CASSCF in cases where comparable DMET calculations fail. Our results for test calculations on the nitrogen double-bond dissociation potential energy curves of several diazene molecules suggest that LASSCF can be an appropriate starting point for a perturbative treatment. Outside of the context of embedding, the LAS wave function is inherently an attractive alternative to a CAS wave function because of its favorable cost scaling, which is exponential only with respect to the size of individual fragment active subspaces, rather than the whole active space of the entire system.

Fragmentation of Valence and Carbon Core Excited and Ionized CH2FCF3 Molecule.

The photofragmentation dynamics of 1,1,1,2-tetrafluoroethane (R134a) with photon energies from 12 eV up to 320 eV, surrounding the C 1s edge is discussed. The ionic moieties were measured in coincidence with the ejected electrons (PEPICO mode), and detected as a function of the photon energy. Around the C K core edge, the fragmentation profiles are examined regarding the site specific excitation of the CH2FCF3 molecule. In the present case, site-selectivity is favored by the distinct chemical environments surrounding both C atoms. NEXAFS spectrum at the C 1s edge simulation has been obtained at the TDDFT level and excited state geometry optimization calculations have been performed at the inner-shell multiconfigurational self-consistent field level. Our observations indicate that the C(H2F) 1s excitation to a highly repulsive potential expels a fluorine atom leaving the heavier radical fragment C2F3H2* which relaxes to the fundamental state of the ion C2F3H2+. On the other hand, the excitation from the C(F3) 1s carbon to a repulsive state in the C-C bond, leads to a C-C bond cleavage, explaining the observed site specific fragmentation.

A study for hydrogen-like lawrencium

Studying hydrogenic ions with high Z is an occasion to understand atomic structure. It also provides a reliable test of methods used to determine atomic structures. Many fields and applications require precise atomic data. For this reason, a hydrogen-like study is performed for lawrencium (Lr102+, Z = 103). The energy levels of hydrogen-like lawrencium are calculated with both multiconfiguration Hartree–Fock (MCHF) and multiconfiguration Dirac–Fock (MCDF) methods. The calculations contain Breit–Pauli relativistic corrections in MCHF calculation and the transverse photon and quantum electrodynamics (QED) effects in MCDF calculation along with electron correlations. In addition, some transition parameters (wavelengths, λ, logarithmic weighted oscillator strengths, log(gf) value, and transition probabilities, Aki) for allowed (E1) and forbidden (E2 and M1) transitions are investigated. The results from this study are compared with only a few theoretical works, but there is no available experimental data yet for Lr102+.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents.

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus 14N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the 14N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

Electron Scattering from Neutral Fe and Low-energy Photodetachment of Fe−

Abstract Extensive calculations are reported for electron collision strengths and rate coefficients for a wide range of transitions in Fe i. The calculations were carried out with the B-spline R-matrix method. A multiconfiguration Hartree–Fock method with nonorthogonal, term-dependent orbitals was employed to generate accurate initial- and final-state wave functions. The close-coupling expansion contained 221 LS states of Fe and included all levels of the , , , , and configurations. Effective collision strengths were obtained by averaging the electron collision strengths over a Maxwellian speed distribution at electron temperatures ranging from 102 to 105 K. They were tabulated for 24,531 transitions between all LS-terms included in the close-coupling expansion. The present results considerably expand on the few existing data sets for Fe i. They enable more detailed treatments of the available measured spectra from various observatories than previously possible. In particular, nonlocal thermodynamic equilibrium modeling of late-type stars, where large amounts of collisional data for the atomic species of interest are required, can be performed. The same close-coupling expansion was used to study low-energy photodetachment of Fe−, where the cross sections exhibit prominent resonance features. Good agreement with the few existing experimental values for partial cross sections to specific final target states of Fe was obtained.

Atomic versus molecular Auger decay in CH2Cl2 and CD2Cl2 molecules.

Autoionization spectra of CH2Cl2 and CD2Cl2 molecules after Cl 2p excitation are studied. The two molecular and atomic Auger transitions are examined and assigned. The contribution of atomic Auger transitions is lower in the deuterated molecule. In addition, to support the presence of the ultrafast dissociation mechanism in the dichloromethane molecule, a series of high-level ab initio quantum mechanical calculations were performed at multiconfigurational self-consistent field (MCSCF) and multireference configuration interaction (MRCI) levels of theory. Minimum energy pathways for the dissociation of the dichloromethane molecule have been calculated by taking into account the spin-orbit splitting between the singlet and triplet transitions in the Cl 2p edge.

Combining Wave Function Methods with Density Functional Theory for Excited States.

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

The photoelectron spectra of the isomeric 1- and 2-methyltetrazoles; their equilibrium structures and vibrational analysis by ab initio calculations.

New synchrotron based studies of the photoelectron ionization spectra (PES) for the isomeric 1- and 2-methyltetrazoles (1- and 2-MeTet) show markedly higher resolution than previous reports. The unusual spectral profiles suggest that a considerable overlay of the ionic states occurs for both molecules. Under these circumstances of near degeneracy of two or more ionic states, mutual annihilation of vibrational fine structure occurs for all except the strongest vibrational states; the PES just reflects the resultants rather than full spectra. Theoretical determination of the adiabatic ionization energies (AIEs) proved a challenge; the most successful method was second order Møller-Plesset perturbation theory (MP2). These calculations suggest that the lowest PES bands for both isomers contain ionization both from lone pair σ-orbitals (2A') on the N-atoms (LPN) and π-orbitals (2A″). The lowest experimental AIEs are as follows: 1-MeTet is 10.315 eV assigned to 12A', while 2-MeTet is 10.543 eV assigned to 12A″. Franck-Condon analysis shows that the lowest ionization energy regions of both spectra are dominated by IE from the LPN2A' manifold, even though the 2A″ states have a higher absolute intensity. In this example, we have utilized a VUV Rydberg state to assist simplification of the PES; more frequently, the PES assignment is simpler and assists the location of Rydberg states in the VUV. The very slow spectral onset for 2-MeTet demonstrates the importance of vertical ionization energy calculations since maxima are more readily measured than slow onsets. These were performed at the equilibrium structure of the X1A' state, using both multi-reference multi-root configuration interaction and the ionization potential variant of the equations-of-motion coupled cluster method, with single and double excitations (EOMIP-CCSD). This enabled the principal ionization bands to be identified over a wider range of energy. Attempts to study the higher ionic states by EOMIP-CCSD showed that several states of each symmetry are close to degenerate for 1-MeTet, in particular. A multi-configuration self-consistent field study confirmed the small separation of ionic states, but state switching during the optimization process largely disabled this method.

Spectroscopy of gold atoms and gold oligomers in helium nanodroplets.

The 6p 2P1/2 ← 6s 2S1/2 and 6p 2P3/2 ← 6s 2S1/2 transitions (D lines) of gold atoms embedded in superfluid helium nanodroplets have been investigated using resonant two-photon ionization spectroscopy. Both transitions are strongly blue-shifted and broadened due to the repulsive interaction between the Au valence electron and the surrounding helium. The in-droplet D lines are superimposed by the spectral signature of Au atoms relaxed into the metastable 2D states. These features are narrower than the in-droplet D lines and exhibit sharp rising edges that coincide with bare atom transitions. It is concluded that they originate from metastable 2D state AuHen exciplexes that have been ejected from the helium droplets during a relaxation process. Interestingly, the mechanism that leads to the formation of these complexes is suppressed for very large helium droplets consisting of about 2 × 106 He atoms, corresponding to a droplet diameter on the order of 50 nm. The assignment of the observed spectral features is supported by ab initio calculations employing a multiconfigurational self-consistent field method and a multi-reference configuration interaction calculation. For large helium droplets doped with Au oligomers, excitation spectra for mass channels corresponding to Aun with n = 2, 3, 4, 5, 7, and 9 are presented. The mass spectrum reveals even-odd oscillations in the number of Au atoms that constitute the oligomer, which is characteristic for coinage metal clusters. Resonances are observed close by the in-droplet D1 and D2 transitions, and the corresponding peak forms are very similar for different oligomer sizes.

Electron-impact excitation of forbidden and allowed transitions in Fe ii

Extensive calculations are reported for electron collision strengths, rate coefficients, and transitions probabilities for a wide range of transitions in Fe ii. The collision strengths were calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and a semiempirical fine-tuning procedure is employed for an accurate representation of the target wave functions. The energy correction was also used in the scattering calculations by adding to Hamiltonian matrices prior to transformation to intermediate coupling. The spin-orbit interaction term was added to the final Hamiltonian matrices in scattering calculations. The close-coupling expansion contains 340 fine-structure levels of Fe ii and includes all levels of the $3{d}^{6}4s$, $3{d}^{5}4{s}^{2}$, $3{d}^{7}$, and $3{d}^{6}4p$ configurations, plus a few lowest levels of the $3{d}^{5}4s4p$ configuration. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities at electron temperatures in the range from ${10}^{2}$ to ${10}^{5}$ K and are reported for all possible inelastic transitions between the 340 fine-structure levels. The present results are more extensive than the previous calculations and considerably expand the existing data sets for Fe ii, allowing a more detailed treatment of the available measured spectra from different space observatories. Comparison with other calculations for collision rates and available experimental radiative rates is used to place uncertainty bounds on our collision strengths and to assess the likely uncertainties in the existing data sets.

The Electric Dipole Transitions of Hydrogen Like Nobelium

It is an occasion to understand and test the methods for determination of atomic structure on hydrogen like ions especially with high atomic number, Z. Many studies such as interpretation of astrophysical spectra and atomic collision studies, the development of X-ray lasers etc. demand exact transition parameters data. This need is a reason of the present paper to support more precise atomic data of electric dipole transitions parameters for hydrogen like nobelium (No 101+ , Z=102). The wavelengths, logarithmic weighted oscillator strengths and transition probabilities of No 101+ have been reproduced with relativistic multiconfiguration Hartree-Fock (MCHF) and fully relativistic multiconfiguration Dirac-Fock (MCDF) methods. The transitions between nl ( n =1-9 and l =0-4) levels have been investigated in this work. The results of MCHF and MCDF methods have been compared with a unique theoretical work, because there has been neither theoretical nor experimental work in available literature.

Ab initio calculations of the hyperfine structure of zinc and evaluation of the nuclear quadrupole moment Q(Zn67)

The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a quasi-statistical approach - the calculations had been carried out with eleven different methods, and then the error bar has been estimated from the differences between the results obtained with those methods.