Relativistic Effects in the Electronic Structure of Atoms.

Periodic trends in relativistic effects are investigated from 1H through 103Lr using Dirac-Hartree-Fock and nonrelativistic Hartree-Fock calculations. Except for 46Pd (4d10) (5s0), all atoms have as outermost shell the ns or n'p spinors/orbitals. We have compared the relativistic spinor energies with the corresponding nonrelativistic orbital energies. Apart from 24Cr (3d5) (4s1), 41Nb (4d4) (5s1), and 42Mo (4d5) (5s1), the ns+ spinor energies are lower than the corresponding ns orbital energies for all atoms having ns spinor (ns+) as the outermost shell, as some preceding works suggested. This indicates that kinematical effects are larger than indirect relativistic effects (the shielding effects of the ionic core plus those due to electron-electron interactions among the valence electrons). For all atoms having np+ spinors as their outermost shell, in contrast, the np+ spinor energies are higher than the corresponding np orbital energies as again the preceding workers suggested. This implies that indirect relativistic effects are greater than kinematical effects. In the neutral light atoms, the np- spinor energies are close to the np+ spinor energies, but for the neutral heavy atoms, the np- spinor energies are considerably lower than the np+ spinor energies (similarly, the np- spinors are considerably tighter than the np+ spinors), indicating the importance of the direct relativistic effects in np-. In the valence nd and nf shells, the spinor energies are always higher than the corresponding orbital energies, except for 46Pd (4d10) (5s0). Correspondingly, the nd and nf spinors are more diffuse than the nd and nf orbitals, except for 46Pd.

Polysulfides protect SH-SY5Y cells from methylglyoxal-induced toxicity by suppressing protein carbonylation: A possible physiological scavenger for carbonyl stress in the brain.

The formation of advanced glycation end products (AGEs) is associated with various neurological disorders, such as Alzheimer's disease, Parkinson's disease and schizophrenia. Methylglyoxal (MG), a highly reactive dicarbonyl compound, is known to be a major precursor for AGEs in modified proteins. Thus, a scavenger of MG might provide beneficial effects by suppressing the accumulation of AGEs and the occurrence of diseases induced by carbonyl stress. Meanwhile, polysulfides, one of the typical bound sulfur species, are oxidized forms of hydrogen sulfide (H2S) and may play a variety of roles in the brain. Herein, we assessed the scavenging ability of polysulfides against neuronal carbonyl stress induced by MG. First, we showed that polysulfides could protect differentiated (df)-SH-SY5Y cells from MG-induced cytotoxicity. When cells were pretreated with polysulfides, MG-induced cytotoxicity was attenuated with a rapid decrease in intracellular MG levels. Moreover, we found that polysulfides significantly suppressed the formation of MG-modified proteins in df-SH-SY5Y cells. Although polysulfide treatment increased endogenous GSH levels in the neuronal cells, its effects on MG-induced cytotoxicity were not affected by GSH concentration. Our results demonstrated that polysulfides had the direct potentials to protect neuronal cells against MG separate to the enzymatic detoxification system that required GSH.

Electronic spectra of DyF studied by four-component relativistic configuration interaction methods.

The electronic states of the DyF molecule below 3.0 eV are studied using 4-component relativistic CI methods. Spinors generated by the average-of-configuration Hartree-Fock method with the Dirac-Coulomb Hamiltonian were used in CI calculations by the KRCI (Kramers-restricted configuration interaction) program. The CI reference space was generated by distributing 11 electrons among the 11 Kramers pairs composed mainly of Dy [4f], [6s], [6p] atomic spinors, and double excitations are allowed from this space to the virtual molecular spinors. The CI calculations indicate that the ground state has the dominant configuration (4f(9))(6s(2))(Ω = 7.5). Above this ground state, 4 low-lying excited states (Ω = 8.5, 7.5, 7.5, 7.5) are found with dominant configurations (4f(10))(6s). These results are consistent with the experimental studies of McCarthy et al. Above these 5 states, 2 states were observed at T0 = 2.39 eV, 2.52 eV by McCarthy et al. and were named as [19.3]8.5 and [20.3]8.5. McCarthy et al. proposed that both states have dominant configurations (4f(9))(6s)(6p), but these configurations are not consistent with the large Re's (∼3.9 a.u.) estimated from the observed rotational constants. The present CI calculations provide near-degenerate states of (4f(10))(6p3/2,1/2), (4f(10))(6p3/2,3/2), and (4f(9))(6s)(6p3/2,1/2) at around 3 eV. The former two states have larger Re (3.88 a.u.) than the third, so that it is reasonable to assign (4f(10))(6p3/2,1/2) to [19.3]8.5 and (4f(10))(6p3/2,3/2) to [20.3]8.5.

Electronic structure of CeO studied by a four-component relativistic configuration interaction method.

We studied the ground and excited states of CeO using the restricted active space CI method in the energy range below 25,000 cm(-1). Energy levels are computed to within errors of 2700 cm(-1). Electron correlation effects arising from the ionic core composed of Ce5s, 5p, 4f(*), 5d(*), and O2s, 2p spinors play crucial role to CeO spectra, as well as correlation effects of electrons distributed in the valence Ce 4f, 5d, 6s, and 6p spinors. Here, 4f(*) and 5d(*) denote spinors expanded to describe electron polarization between Ce and O. A bonding mechanism is proposed for CeO. As the two separate atoms in their ground states, Ce(4f(1)5d(1)6s(2))(1)G4 and O(2s(2)2p(4))(3)P2, approach each other, a CeO(2+) core is formed by two-electron transfer from Ce5d, 6s to O2p. Inside this ellipsoidal ion, a valence bond between Ce5p and O2s and an ionic bond between O2p and Ce5p are formed with back-donation through Ce 4f(*) and 5d(*).

Cu 4s → 4p atomic like excitations in the Ne matrix.

The lowest three or four excited states (the triplet or quartet states) of the Cu atom in a neon (Ne) matrix have been studied experimentally, and have been presumed to have the electronic configuration of Cu 4p(1). The origins of the triplet and the quartet are not yet fully clear, although many models have been proposed. It has been argued, for example, that the existence of different trapping sites would give rise to two partly overlapping triplets, leading to spectra having three or four lines or more. Below, the electronic structures of the ground state and lowest excited states of the Cu atom in the neon matrix are clarified by means of ab initio molecular orbital calculations, using the cluster model. It was found that a rather large vacancy (hollow) with residual Ne atoms is vital for explaining the observed spectra having three or more lines; the Cu atom occupies the center of the substitutional site of a face-centered cubic (fcc)-like cluster comprising 66 Ne atoms, in which the first shell composed of 12 Ne atoms is empty. The presence of the residual Ne atoms in the first shell gives rise to more than three excited states, explaining the experimental spectra. Electron-electron interaction (including the crystal field) and spin-orbit interaction are both important in explaining the experimental spectra.

Electronic spectra of GdF reanalyzed by decomposing state functions according to f-shell angular momentum.

The electronic structure of the GdF molecule was studied by means of four-component relativistic configuration interaction (CI) calculations [S. Yamamoto, H. Tatewaki, and T. Saue, J. Chem. Phys. 129, 244505 (2008)]. To analyze the electronic spectra more accurately, the CI wave function is decomposed according to the angular momentum (Ω(f)) generated from the (4f)(7) electrons. The weight of a specified Ω(f) is referred to as the "f-shell Omega component weight." This Ω(f) plays a crucial role in classifying the strong electronic transitions from the upper states (0.7 eV-3.0 eV) to the lower states (~0.55 eV). For these transitions, the upper and lower states have almost identical Ω(f) weights. This appears to be a necessary condition for a transition to be strong. The same condition is expected to hold for other lanthanide linear molecules. A point charge model is also studied, acting as a simplified model of GdF; it successfully reproduces the spectra of GdF, justifying studies based on ligand field theory.

Electronic structure of LaO based on frozen-core four-component relativistic multiconfigurational quasidegenerate perturbation theory.

The electronic structure of the LaO molecule is studied using frozen-core four-component multiconfigurational quasidegenerate perturbation theory. The ground state and nine experimentally observed excited states are examined. The ground state is (2)Sigma(1/2)(+) and its gross atomic orbital population is La(5p(5.76)6s(0.83)6p(0.14)p(*(0.21) )d(*(1.17) )f(*(0.26) )) O(2p(4.63)), where p*, d*, and f* are the polarization functions of La that form molecular spinors with O 2ps. We found that it is not necessary to consider the excitation from the O 2p electrons when analyzing the experimental spectra. This validates the foundation of the ligand field theory on diatomic molecules, including the La atom where only one electron is considered. The spectroscopic constants R(e), omega(e), and T(0) calculated for the ground state and low-lying excited states A'((2)Delta(3/2)), A'((2)Delta(5/2)) A((2)Pi(1/2)), and A((2)Pi(3/2)) are in good agreement with the experimental values.

Excited states of PbF: a four-component relativistic study.

The electronic states of lead monofluoride (PbF) are studied from the (Pb 6s)(2) (F 2p-pi)(4) (F 2p-sigma)(2) (Pb 6p-pi)(1) X(1) ground state up to the F state, using the four-component relativistic configuration interaction and Fock-space coupled-cluster singles and doubles methods. Difficulties arising from the valence-Rydberg mixing are overcome by using a flexible basis set including Rydberg-type diffuse functions and by large-scale correlation calculations. The excited states are successfully characterized with the help of computed transition dipole moments. The three lowest-lying states (X(1), X(2), and A) are confirmed to be valence states arising from the (Pb 6p) spinors. The B state is assigned to the lowest Rydberg state (Omega=1/2), represented by a single excitation from the (Pb 6p-pi) spinor to the (F 3s) Rydberg spinor. Its calculated excitation energy (4.30 eV) is comparable to the observed one (4.42 eV). The C state is a multiconfigurational valence state whose dominant configuration is represented by (Pb 6s)(2) (F 2p-pi)(4) (F 2p-sigma)(1) (Pb 6p-pi)(2). Its calculated excitation energy (4.71 eV) is in good agreement with experiment (4.72 eV). The remaining D, E, and F states are assigned as Rydberg states. The calculated ionization potential (7.44 eV) is also close to the value (7.55 eV) determined recently by multiphoton ionization experiments.

Intruder states in multireference perturbation theory: the ground state of manganese dimer.

A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states (> 5000) do not permit finding even an approximate shape of the X(1)Sigma(g) (+) potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the X(1)Sigma(g) (+) state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in MS-MRPT. Various alternative approaches of removing intruder states (e.g., modification of the basis set or changing the active space) are tested. None of these conventional techniques is able to fully avoid the quasidegeneracies. We believe that the MS-MRPT calculations on the three lowest A(g) states of manganese dimer constitute a perfect benchmark case for studying the behavior of MRPT in extreme situations.

Choosing a proper complete active space in calculations for transition metal dimers: ground state of Mn2 revisited.

The potential energy curve of the ground state of Mn(2) has been studied using a systematic sequence of complete active spaces. Deficiencies of the routinely used active space, built from atomic 4s and 3d orbitals, has been identified and discussed. It is shown that an additional sigma(g) orbital, originating from the atomic virtual 4p(z) orbitals, is essential for a proper description of static correlation in the (1)Sigma(g)(+) state of Mn(2). The calculated spectroscopic parameters of the (1)Sigma(g)(+) state agree well with available experimental data. The calculated equilibrium bond lengths are located between 3.24 and 3.50 A, the harmonic vibrational frequencies, between 44 and 72 cm(-1), and the dissociation energies, between 0.05 and 0.09 eV. An urgent need for an accurate gas-phase experimental study of spectroscopic constants of Mn(2) is highlighted.

Electronic structure of CeF from frozen-core four-component relativistic multiconfigurational quasidegenerate perturbation theory.

We have investigated the ground state and the two lowest excited states of the CeF molecule using four-component relativistic multiconfigurational quasidegenerate perturbation theory calculations, assuming the reduced frozen-core approximation. The ground state is found to be (4f(1))(5d(1))(6s(1)), with Omega = 3.5, where Omega is the total electronic angular momentum around the molecular axis. The lowest excited state with Omega = 4.5 is calculated to be 0.104 eV above the ground state and corresponds to the state experimentally found at 0.087 eV. The second lowest excited state is experimentally found at 0.186 eV above the ground state, with Omega = 3.5 based on ligand field theory calculations. The corresponding state having Omega = 3.5 is calculated to be 0.314 eV above the ground state. Around this state, we also have the state with Omega = 4.5. The spectroscopic constants R(e), omega(e), and nu(1-0) calculated for the ground and first excited states are in almost perfect agreement with the experimental values. The characteristics of the CeF ground state are discussed, making comparison with the LaF(+) and LaF molecules. We denote the d- and f-like polarization functions as d(*) and f(*). The chemical bond of CeF is constructed via {Ce(3.6+)(5p(6)d(*0.3)f(*0.1))F(0.6-)(2p(5.6))}(3+) formation, which causes the three valence electrons to be localized at Ce(3.6+).

Dipole allowed transitions in GdF: A four-component relativistic general open-shell configuration interaction study.

A four-component relativistic study of electronic transitions in the gadolinium monofluoride molecule (GdF) is presented. The electronic spectra of GdF have been investigated with a general open-shell configuration interaction method, where active electrons are distributed among molecular spinors mainly consisting of the Gd 4f, 5d, and 6s atomic spinors. The near-degeneracy effects of these spinors on the molecular electronic structure are considered by the valence full-CI-like approach. By the magnitudes of calculated transition dipole moments, the candidates for the observable transitions were selected. The present result is complementary to our previous study based on multireference configuration interaction singles and doubles calculations, which identified the electronic excited states of GdF by comparing the calculated excitation energies and angular momenta with those given by the laser spectroscopy. The spectra of the excited states less than 3.0 eV have been refined with the help of the calculated transition probabilities. The transitions between the excited states are newly analyzed and a rearrangement is proposed.

Electronic structure of the GdF molecule by frozen-core four-component relativistic configuration interaction calculations.

The electronic structure of GdF is calculated based on frozen-core four-component relativistic configuration interactions. The resulting excitation energies are fairly close to experiment and correctly designate the excited states. For instance, the existence of the experimentally inferred state at 0.55 eV above the ground state is confirmed, having Omega=132 with (4f(7)5d(+) (1)6s(+) (1)); it is 0.58 eV above the ground state according to the present calculation.

Gaussian-type function set without prolapse for the Dirac-Fock-Roothaan equation (II): 80Hg through 103Lr.

We present prolapse-free universal Gaussian-type basis sets for 80Hg through 103Lr. The basis set is determined so that the Dirac-Fock-Roothaan total energy should decrease monotonically toward the numerical Dirac-Fock total energy. The difference between the Dirac-Fock-Roothaan total energy and the numerical Dirac-Fock total energy is less than 3 x 10(-6) hartree for 1H through 102No, and less than 5 x 10(-6) hartree for 103Lr. The exponents of the present sets are determined in an even-tempered manner, aiming to give total energy closer to the numerical Dirac-Fock value as the expansion term increases. The recommended set is expanded by (64, 64, 64, 46, 46, 46, 46) terms for (s+, p-, p+, d-, d+, f-, f+) symmetries, respectively. A practical set with (56, 48, 48, 36, 36, 36, 36) terms is also presented.

A study of the ground state of manganese dimer using quasidegenerate perturbation theory.

We study the electronic structure of the ground state of the manganese dimer using the state-averaged complete active space self-consistent field method, followed by second-order quasidegenerate perturbation theory. Overall potential energy curves are calculated for the 1Sigmag+, 11Sigmau+, and 11Piu states, which are candidates for the ground state. Of these states, the 1Sigmag+ state has the lowest energy and we therefore identify it as the ground state. We find values of 3.29 A, 0.14 eV, and 53.46 cm(-1) for the bond length, dissociation energy, and vibrational frequency, in good agreement with the observed values of 3.4 A, 0.1 eV, and 68.1 cm(-1) in rare-gas matrices. These values show that the manganese dimer is a van der Waals molecule with antiferromagnetic coupling.

Characterization of molecular orbitals by counting nodal regions.

The number of nodal regions can be used as an index for characterizing molecular orbitals. A computer program has been developed to count the number of nodal regions, based on the labeling and contraction algorithms. This program is applied to the water molecule, the hydrogen sulfide molecule, the hydrogen atomic orbitals, the Rydberg excited states of ethylene, dissociation of carbon monoxide, and CASSCF calculations of formaldehyde. Because the number of nodal regions is independent of the coordinate system, the method is applicable even when the molecular structure changes drastically as in bond rotation or bond elongation. Changes of nodal regions with bond elongation are investigated for carbon monoxide. A prescription for problems arising with basis set expansion techniques is also given.

Quality of contracted Gaussian-type function basis sets.

The valence quality of contracted (C) Gaussian-type function (GTF) basis sets in molecular calculations is discussed for the first- through fourth-row atoms. The split-valence basis sets derived from minimal-type CGTF sets are compared with those derived from primitive (P) GTF sets. Using F, Cl, Br, and I atoms and their homonuclear diatomics as test species, we find that the split-valence CGTF sets have almost the same quality as PGTF sets with larger s and p expansion terms: for example, the (53/5), (533/53), (5333/533/5), and (53 333/5333/53) CGTF sets correspond approximately to the [9/5], [15/9], [19/15/5], and [22/18/7] PGTF sets for the first- to fourth-row atoms, respectively, where the slash separates the s, p, and d symmetries. For the main group atoms of the four rows, we recommend using the above-mentioned CGTFs or larger.

Torsion potential works in rhodopsin.

We investigate the role of protein environment of rhodopsin and the intramolecular interaction of the chromophore in the cis-trans photoisomerization of rhodopsin by means of a newly developed theoretical method. We theoretically produce modified rhodopsins in which a force field of arbitrarily chosen part of the chromophore or the binding pocket of rhodopsin is altered. We compare the equilibrium conformation of the chromophore and the energy stored in the chromophore of modified rhodopsins with those of native rhodopsins. This method is called site-specific force field switch (SFS). We show that this method is most successfully applied to the torsion potential of rhodopsin. Namely, by reducing the twisting force constant of the C11=C12 of 11-cis retinal chromophore of rhodopsin to zero, we found that the equilibrium value of the twisting angle of the C11=C12 bond is twisted in the negative direction down to about -80 degrees. The relaxation energy obtained by this change amounts to an order of 10 kcal/mol. In the case that the twisting force constant of the other double bond is reduced to zero, no such large twisting of the bond happens. From these results we conclude that a certain torsion potential is applied specifically to the C11=C12 bond of the chromophore in the ground state of rhodopsin. This torsion potential facilitates the bond-specific cis-trans photoisomerization of rhodopsin. This kind of the mechanism is consistent with our torsion model proposed by us more than a quarter of century ago. The origin of the torsion potential is analyzed in detail on the basis of the chromophore structure and protein conformation, by applying the SFS method extensively.