Relativistic Density Functional Theory Calculations Research Articles

Bonding and Magnetic Response Properties of Several Toroid Structures. Insights of the Role of Ni2S2 as a Building Block from Relativistic Density Functional Theory Calculations

Relativistic density functional calculations were carried out on several nickel toroid mercaptides of the general formula [Ni(μ-SR)(2)](n), with the aim to characterize and analyze their stability and magnetic response properties, in order to gain more insights into their stabilization and size-dependent behavior. The Ni-ligand interaction has been studied by means projected density of states and energy decomposition analysis, which denotes its stabilizing character. The graphical representation of the response to an external magnetic field is applied for the very first time taking into account the spin-orbit term. This map allows one to clearly characterize the magnetic behavior inside and in the closeness of the toroid structure showing the prescence of paratropic ring currents inside the Ni(n) ring, and by contrast, diatropic currents confined in each Ni(2)S(2) motif denoting an aromatic behavior (in terms of magnetic criteria). The calculated data suggests that the Ni(2)S(2) moiety can be regarded as a stable constructing block, which can afford several toroid structures of different nuclearities in agreement with that reported in the experimental literature. In addition, the effects of the relativistic treatment over the magnetic response properties on these lighter compounds are denoted by comparing nonrelativistic, scalar relativistic, and scalar plus spin-orbit relativistic treatments, showing their acting, although nonpronunced, role.

Toward an Understanding of Ligand Selectivity in Nanocluster Synthesis

We performed scalar relativistic density functional theory (DFT) calculations using the projector augmented wave scheme (PAW) to examine the reactivity and selectivity of diphosphine ligands LM, with the formula PH2(CH2)MPH2 (spacer M = 3, 5), toward small-sized cationic Aun (n = 7–11) nanoclusters. By isolating the ligand-induced contribution to the stability condition, we show that such interaction selectively stabilizes the cationic Au11 cluster. Furthermore, we find that L5 with the longer spacer is more capable than L3 of relieving the strain imposed on the spacer by bidentate binding to gold clusters, which have relatively small Au–Au bond lengths. Thus L5 can interact effectively with gold clusters of various sizes, but L3 can do so only with a selected few. This result demonstrates the size-selecting power of L3 toward small gold clusters such as Au113+. To further test the validity of our results we have extended the calculation to a larger cluster, Au13, and also considered the case of a ligand ...

Spin–orbit coupling effect on Au–C60 interaction: A density functional theory study

Density functional theory (DFT) calculations with relativistic spin–orbit (SO) effect are performed to exohedral Au–C60 and Au2–C60–Au2 complexes. The optimal interaction patterns are identified. SO effect tends to enhance the Au–C60 interaction and depends on both Au–C distance and Au–C bonding. However, inclusion of SO effect has only limited impact on the relative stability of Au–C60 isomers that is predicted by scalar relativistic DFT calculations because the SO enhancement has roughly the same order with the Au–C interacting strength. In addition, the stabilization energy contributed from SO effect tends to increase with Au cluster size.

Photoelectron Imaging and Theoretical Studies of Silver Monohalides AgX– (X = Cl, Br, I) and AuCl–

Photodetachment of AgX(-) (X = Cl, Br, I) and AuCl(-) is studied by a photoelectron velocity map imaging technique and theoretical calculations. Photoelectron spectra (PES) and photoelectron angular distributions (PADs) were obtained. The vibrationally resolved spectra provided approximately equal electron affinities (EAs) for AgX: 1.593(22) eV for AgCl, 1.623(21) eV for AgBr, and 1.603(22) eV for AgI, respectively. Franck-Condon simulations of these spectra gave the equilibrium bond lengths and vibrational frequencies of the title anions. Relativistic density functional theory (DFT) calculations using BLYP, PW91, PBE, and BP86 functionals have been performed to predict the EAs of the AgX (X = Cl, Br, I) molecules. The computed EAs at the BP86 level of theory are in good agreement with the experimental values. Energy partitioning analyses (EPA) at the BP86(ZORA)/QZ4P level of theory of both anions and their neutrals were reported.

Magnetic Properties of Monomer and Dimer Tetrahedral VO(x) Entities Dispersed on Amorphous Silica-based Materials: Prediction of EPR Parameters from Relativistic DFT Calculations and Broken Symmetry Approach to Exchange Couplings.

Molecular structures of the isolated tetrahedral oxovanadium(IV) and bridged μ-oxo-divanadium(IV) complexes hosted by the clusters mimicking surfaces of amorphous silica-based materials were investigated using density functional theory (DFT) calculations. Principal values of the g and A tensors for the monomer vanadyl species were obtained using the coupled-perturbed DFT level of theory and the spin–orbit mean-field approximation (SOMF). Magnetic exchange interaction for the μ-oxo bridged vanadium(IV) dimer was investigated within the broken symmetry approach. An antiferromagnetic coupling of the individual magnetic moments of the vanadium(IV) centers in the [VO–O–VO]2+ bridges was revealed and discussed in detail. The coupling explains pronounced decrease of the electron paramagnetic resonance signal (EPR) intensity, observed for the reduced VOx/SiO2 samples with the increasing coverage of vanadia, in terms of transformation of the paramagnetic monomer species into the dimers with S = 0 ground state.

Experimental and theory studies of the oxidation reaction of neutral gold carbonyl clusters in the gas phase

Neutral gold carbonyl clusters, Au m (CO) n ( m = 3–9, n = 2–7, m ≥ n), are generated by laser ablation of Au into a mixture of CO/He, cooled in a supersonic expansion, and reacted with O 2 and N 2O in a fast flow reactor. The neutral reactants and products are detected in a time of flight mass spectrometer through single photon ionization by a 193 nm laser. Signal intensities of Au 3(CO) 2,3, Au 5(CO) 4, and Au 7(CO) 4,5 decrease significantly following reaction of these clusters with O 2 in the fast flow reactor; only Au 3(CO) 2 and Au 3(CO) 3 signals decrease moderately following reaction with N 2O. The reaction cross section for Au m (CO) n with N 2O is significantly smaller than that with O 2. Density functional theory calculations with and without explicit consideration of relativistic effects are performed to investigate the reaction mechanisms for the oxidation of Au 3(CO) 2 and Au 3(CO) 3 clusters with O 2 and N 2O. Both calculational algorithms predict a considerable barrier for the reactions of Au 3(CO) 2,3 with N 2O. Non relativistic density functional theory calculations predict a positive overall barrier for the reactions of Au 3(CO) 2,3 with O 2, in disagreement with experimental observations. Relativistic density functional theory calculations for the reactions Au 3(CO) 2,3 with O 2 predict that they are thermodynamically allowed, although the barrier heights are not in the appropriate order to support the apparent relative reactivities of Au 3(CO) 2 and Au 3(CO) 3 with O 2.

Spin Ground State and Magnetic Properties of Cobalt(II): Relativistic DFT Calculations Guided by EPR Measurements of Bis(2,4-acetylacetonate)cobalt(II)-Based Complexes

The spin ground state of the core ion and structure of the bis(2,4-acetylacetonate)cobalt(II) model complex and its synthetic aqua and ethanol derivatives, Co(acac)(2)L(n), (L = EtOH, H(2)O), were examined by means of density functional theory (DFT) calculations supported by electron paramagnetic resonance (EPR) measurements. Geometry optimizations were carried out for low-spin (doublet) and high-spin (quartet) states. For the Co(acac)(2) complex two possible conformations, a square-planar and a tetrahedral one, were taken into account. For all structures relative energies were calculated with both "pure" and hybrid functionals. The calculated data were complemented with the results of the EPR investigations carried out at liquid helium temperature, allowing for definite assignment of the high-spin state for the Co(acac)(2)(EtOH)(2) complex. However, because of the unresolved spectral features, only effective g-values could be assessed, whereas the zero-field splitting parameters (ZFS) were calculated by means of the spin-orbit mean field (SOMF) relativistic DFT method for which direct spin-spin (SS) and spin-orbit coupling (SOC) contributions were quantified.

Structures and energetics of small lead cluster ions

By a combination of gas phase ion mobility measurements and relativistic density functional theory calculations with inclusion of spin-orbit coupling, we assign structures of lead cluster cations and anions in the range between 4 and 15 atoms. We find a planar rhombus for the tetramer, a trigonal bipyramid for the pentamer, and a pentagonal bipyramid for the heptamer, independent of charge state. For the hexamer, the cation and anion structures differ: we find an octahedron for the anion while the cation consists of fused tetrahedra. For the octamer, we find in both cases structures based on the pentagonal bipyramid motif plus adatom. For the larger clusters investigated we always find different structures for cations and anions. For example, Pb(12)(-) is confirmed to be a hollow icosahedron while Pb(12)(+) is a truncated filled icosahedron. Pb(13)(+) is a filled icosahedron but Pb(13)(-) is a hollow icosahedron with the additional atom capping a face. In order to get experimental information on the relative stabilities, we investigated the collision induced dissociation mass spectra for the different cluster sizes and charge states, and observe a strong correlation with the calculated fragmentation energies. Up to n = 13 the main fragmentation channel is atom loss; for the larger cluster sizes we observe fission into two large fragments. This channel is dominant for larger anions, less pronounced but clearly present for the cations.

Solid-State115In and31P NMR Studies of Triarylphosphine Indium Trihalide Adducts

Solid-state (115)In and (31)P NMR spectroscopy, relativistic density functional theory (DFT) calculations, and single-crystal X-ray diffraction were used to investigate a series of triarylphosphine indium(III) trihalide adducts, X(3)In(PR(3)) and X(3)In(PR(3))(2) (X = Cl, Br or I; PR(3) = triarylphosphine ligand). The electric field gradient tensors at indium as well as the indium and phosphorus magnetic shielding tensors and the direct and indirect (115)In-(31)P spin-spin coupling were characterized; for complexes possessing a C(3) symmetry axis, the anisotropy in the indirect spin-spin coupling, DeltaJ((115)In,(31)P), was also determined. The (115)In quadrupolar coupling constants, C(Q)((115)In), range from +/-1.25 +/- 0.10 to -166.0 +/- 2.0 MHz. For any given phosphine ligand, the indium nuclei are most shielded for X = I and least shielded for X = Cl, a trend also observed for other group-13 nuclei in M(III) complexes. This experimental trend, attributed to spin-orbit effects of the halogen ligands, is reproduced by the DFT calculations. The spans of the indium magnetic shielding tensors for these complexes, delta(11)-delta(33), range from 40 +/- 7 to 710 +/- 60 ppm; those determined for phosphorus range from 28 +/- 1.5 to 50 +/- 3 ppm. Values of (1)J((115)In,(31)P) range from 550 +/- 20 to 2500 +/- 20 Hz. For any given halide, the (1)J((115)In,(31)P) values generally increase with increasing basicity of the PR(3) ligand. Calculated values of (1)J((115)In,(31)P) and DeltaJ((115)In,(31)P) duplicate experimental trends and indicate that both the Fermi-contact and spin-dipolar Fermi-contact mechanisms make important contributions to the (1)J((115)In,(31)P) tensors.

Local structure relaxation, quantum trap depression, and valence charge polarization induced by the shorter-and-stronger bonds between under-coordinated atoms in gold nanostructures

Relativistic density functional theory calculations have been conducted to examine the effect of atomic under-coordination on the crystal structure, binding energy, and electron configuration of cuboctahedral and Marks decahedral gold clusters. Trend consistency between calculations and experimental observations confirmed the predictions made using BOLS correlation theory, suggesting that the shorter-and-stronger bonds between under-coordinated atoms induce local structure relaxation, potential well depression, and the associated local charge and energy densification, as well as the polarization of the otherwise conducting s-electrons (valence charge) by the densely- and tightly-trapped core electrons of which the binding energy shifts positively to deeper energies. Findings are in good agreement with scanning tunneling microscopy/spectroscopy results from monomers, dimers, chain ends, and nanostructures of gold and other metals.

Vibrationally Resolved Photoelectron Spectroscopy of Di-Gold Carbonyl Clusters Au2(CO)n− (n = 1−3): Experiment and Theory

We report vibrationally resolved photoelectron spectroscopy (PES) of Au(2)(CO)(n)(-) (n = 1-3), in combination with relativistic density functional theory (DFT) and ab initio calculations. The ground-state transition in the spectrum of Au(2)CO(-) is broad, containing vibrational structures both in the bending and in the CO stretching modes and suggesting a large structural change from Au(2)CO(-) to Au(2)CO. The ground-state transitions for both n = 2 and 3 display a well-resolved vibrational progression in the CO stretching mode with frequencies of 2110 +/- 40 and 2160 +/- 40 cm(-1), respectively. The PES data show that chemisorption of the first two CO's each induces a significant red-shift in the electron binding energies. The third CO is physisorbed, inducing only a slight increase in electron binding energies relative to Au(2)(CO)(2)(-). Relativistic DFT and ab initio calculations are performed to determine the ground-state structures for Au(2)(CO)(n)(-) and Au(2)(CO)(n), and the results agree well with the experiment. Au(2)(CO), Au(2)(CO)(2), and Au(2)(CO)(2)(-) are all found to be linear, while Au(2)(CO)(-) is bent due to the Renner-Teller effect. A strong spin-orbit effect is found in Au(2)(CO)(2)(-) that quenches the Renner-Teller effect, keeping the linear structure for this anion. The physisorption in Au(2)(CO)(3)(-) is borne out in CCSD(T) calculations. However, a wide range of DFT methods tested fail to correctly predict the relative energies of the physisorbed versus chemisorbed isomers for Au(2)(CO)(3)(-).

Theoretical Studies on Structural, Magnetic, and Spintronic Characteristics of Sandwiched EunCOTn+1 (n = 1−4) Clusters

Europium (Eu)-cyclootetatrene (COT = C(8)H(8)) multidecker clusters (Eu(n)COT(n+1), n = 1-4) are studied by relativistic density functional theory calculations. These clusters are found to be thermodynamically stable with freely rotatable COT rings, and their total magnetic moments (MMs) increase linearly along with the number of Eu atoms. Each Eu atom contributes about 7 mu(B) to the cluster. Meanwhile, the internal COT rings have little MM contribution while the external COT rings have about 1 mu(B) MM aligned in opposite direction to that of the Eu atoms. The total MM of the Eu(n)COT(n+1) clusters can thus be generalized as 7n - 2 mu(B) where n is the number of Eu atoms. Besides, the ground states of these clusters are ferromagnetic and energetically competitive with the antiferromagnetic states, meaning that their spin states are very unstable, especially for larger clusters. More importantly, we uncover an interesting bonding characteristic of these clusters in which the interior ionic structure is capped by two hybrid covalent-ionic terminals. We suggest that such a characteristic makes the Eu(n)COT(n+1) clusters extremely stable. Finally, we reveal that for the positively charged clusters, the hybrid covalent-ionic terminals will tip further toward the interior part of the clusters to form deeper covalent-ionic caps. In contrast, the negatively charged clusters turn to pure ionic structures.

Theoretical Mechanism Study of UF6 Hydrolysis in the Gas Phase (II)

In our previous work (J. Phys. Chem. A 2008, 112, 8877.), we found theoretical evidence indicating UF5OH is an intermediate produced in the first step of UF6 hydrolysis. In this work, we explored the probable reaction channels starting from UF5OH + UF6 and UF5OH + UF5OH systems using relativistic density functional theory calculations. Initially, the two uranium containing species associate to form complex UF6.UF5OH or dimer (UF5OH)2 through hydrogen bonding. The energy released is 12-16 kcal/mol, which may promote further reactions. After H2O or HF are eliminated from the complex or dimer, compounds containing U-O-U bond are produced. These compounds are potentially feasible to associate into larger clusters or solidify. Relative to the isolated initial species, the energies of the final products are -6 to -13 kcal/mol lower, indicating that the reactions may spontaneously proceed. The calculated IR spectra features can be used to indicate the formation and interaction type of the intermediates and products.

Effect of Ligands on the Geometric and Electronic Structure of Au13 Clusters

We have carried out scalar relativistic density functional theory calculations within the projector augmented wave scheme and the pseudopotential approach, to examine the effect of ligands on the geometric and electronic structure of four Au13 isomers: planar, flake, cuboctahedral, and icosahedral clusters. We find, in agreement with previous theoretical calculations, that for the clean cluster the planar geometry has the lowest total energy while the icosahedral and cuboctahedral structures undergo Jahn−Teller distortion. On the other hand, when ligated by phosphines, the icosahedron is found to assume the lowest total energy. The rationale for the stabilization of the icosahedron in the ligated Au13 cluster is traced to the ligand-induced charge transfer from the surface Au−Au to Au-ligand bonds leading to the formation of a strong Au-ligand covalent bond and introduction of a compressive strain which further weakens the Au−Au bonds.

Direct Detection and Characterization of Chloride in the Active Site of the Low-pH Form of Sulfite Oxidase Using Electron Spin Echo Envelope Modulation Spectroscopy, Isotopic Labeling, and Density Functional Theory Calculations

Electron spin echo envelope modulation (ESEEM) investigations were carried out on samples of the low-pH (lpH) form of vertebrate sulfite oxidase (SO) prepared with (35)Cl- and (37)Cl-enriched buffers, as well as with buffer containing the natural abundance of Cl isotopes. The isotope-related changes observed in the ESEEM spectra provide direct and unequivocal evidence that Cl(-) is located in close proximity to the Mo(V) center of lpH SO. The measured isotropic hyperfine interaction constant of about 4 MHz ((35)Cl) suggests that the Cl(-) ion is either weakly coordinated to Mo(V) at its otherwise vacant axial position, trans to the oxo ligand, or is hydrogen-bonded to the equatorial exchangeable OH ligand. Scalar relativistic all-electron density functional theory (DFT) calculations of the hyperfine and nuclear quadrupole interaction parameters, along with steric and energetic arguments, strongly support the possibility that Cl(-) is hydrogen-bonded to the equatorial OH ligand rather than being directly coordinated to the Mo(V).

Metal−Phosphorus Bonding in Complexes W@Au12PX3 (X = H, F, Cl, Br, I, Me, OMe) and [M@Au12]qPH3 (Mq = Hf2−, Ta−, W, Re+, Os2+, Ir3+, Pt4+, Au5+): Relativistic DFT Investigations

Relativistic density functional theory (DFT) calculations of the geometries and Au-P bonding of W@Au(12)PX(3) (X = H, F, Cl, Br, I, Me, OMe) and [M@Au(12)](q)PH(3) (M(q) = Hf(2-), Ta(-), W, Re(+), Os(2+), Ir(3+), Pt(4+), Au(5+)) have been carried out. There are some regular changes in geometry and binding of these two kinds of complexes with the variation of the phosphanes PX(3) and transition metals M(q). The energy decomposition analysis confirms that the PX(3) ligands are sigma donors. The donor tendency (DeltaE(sigma)/DeltaE(pi)) decreases for different X with increasing electronegativity and for different M(q) from Au(5+) to Hf(2-), while the pi-back-donation increases in the same direction. The calculated P-H bond lengths show a regular decrease from Hf(2-) to Ir(3+), but have abnormal trends for Pt(4+) and Au(5+).

Lanthanide(III) and Actinide(III) Complexes [M(BH4)2(THF)5][BPh4] and [M(BH4)2(18-crown-6)][BPh4] (M = Nd, Ce, U): Synthesis, Crystal Structure, and Density Functional Theory Investigation of the Covalent Contribution to Metal-Borohydride Bonding

Treatment of [M(BH4)3(THF)3] with NEt3HBPh4 in THF afforded the cationic complexes [M(BH4)2(THF)5][BPh4] [M = U (1), Nd (2), Ce (3)] which were transformed into [M(BH4)2(18-crown-6)][BPh4] [M = U (4), Nd (5), Ce (6)] in the presence of 18-crown-6; [U(BH4)2(18-thiacrown-6)][BPh4] (7) was obtained from 1 and 18-thiacrown-6 in tetrahydro-thiophene. Compounds 1, 3.C4H8S, 4.THF, 5, and 6.THF exhibit a penta- or hexagonal bipyramidal crystal structure with the two terdentate borohydride ligands in apical positions; the BH4 groups in the crystals of 7.C4H8S are in relative cis positions, and the thiacrown-ether presents a saddle shape, with two diametrically opposite sulfur atoms bound to uranium in trans positions. The crystal structures of these complexes, as well as those of previously reported [M(BH4)2(THF)5]+ cations, do not reveal any clear-cut lanthanide(III)/actinide(III) differentiation. The structural data obtained for [M(BH4)2(18-crown-6)]+ (M = U, Ce) by relativistic density functional theory (DFT) calculations are indicative of a small shortening of the U...B with respect to the Ce...B distance, which is accompanied by a lengthening of the U-Hb bonds and an opening of the Hb-B-Hb angle (Hb = bridging hydrogen atom of the eta3-BH4 ligand). The Mulliken population analysis and the natural bond orbital analysis indicate that the BH4 -->M(III) donation is greater for M = U than for M = Ce, as well as the overlap population of the M-Hb bond, thus showing a better interaction between the uranium 5f orbitals and the Hb atoms. The more covalent character of the B-H-U three-center two-electron bond was confirmed by the molecular orbital (MO) analysis. Three MOs represent the pi bonding interactions between U(III) and the three Hb atoms with significant 6d and 5f orbital contributions. These MOs in the cerium(III) complex exhibit a much lesser metallic weight with practically no participation of the 4f orbitals.

Theoretical Mechanism Study of UF6 Hydrolysis in the Gas Phase

The mechanism of the gas-phase reaction UF 6 + H 2O --> UOF 4 + 2HF is explored using relativistic density functional theory calculations. Initially, H 2O coordinates with UF 6 to form a 1:1 complex UF 6.H 2O. Over an activation energy barrier of about 19 kcal/mol, H 2O transfers a H atom to a nearby ligand F, resulting in UF 5OH + HF. The eliminated HF or another H 2O molecule may form a hydrogen bond with UF 5OH. Starting from UF 5OH, the second HF elimination results in UOF 4. If UF 5OH is in the isolated form, UF 5OH --> UOF 4 + HF takes place over a barrier of 24 kcal/mol. If UF 5OH is hydrogen-bonded with H 2O or HF, the conversion barrier is less than 10 kcal/mol. Once formed, the unstable UOF 4 tends to associate with additional ligands and hydrogen-bonding donors. The calculated binding energies indicate the significance of such interactions, which may have profound impact on further HF eliminating reactions. The IR spectra features can be used to indicate the formation and interaction type of the intermediates and products.

Spin-Orbit Coupling and Ion Displacements in MultiferroicTbMnO3

The magnetic and ferroelectric (FE) properties of TbMnO3 are investigated on the basis of relativistic density functional theory calculations. We show that, due to spin-orbit coupling, the spin-spiral plane of TbMnO3 can be either the bc or ab plane, but not the ac plane. As for the mechanism of FE polarization, our work reveals that the "pure electronic" model by Katsura, Nagaosa, and Balatsky is inadequate in predicting the absolute direction of FE polarization. Our work indicates that to determine the magnitude and the absolute direction of FE polarization in spin-spiral states, it is crucial to consider the displacements of the ions from their centrosymmetric positions.

Properties of Pt-supported Co nanomagnets from relativistic density functional theory calculations

The electronic, structural, and magnetic properties of Co-based low-dimensional nanostructures supported by Pt surfaces are investigated using computer simulations based on density functional theory. The effects of the local orientation of the magnetization, including the magnetic anisotropy energy, are accounted for within a noncollinear spin-density functional theory formalism where the spin-orbit interaction is described by fully relativistic ultrasoft pseudopotentials. The magnetic moments, the direction of the easy-magnetization axis, and the anisotropy energy are compared with available experimental and theoretical data, and are shown to be extremely sensitive to the local atomic environment of the Co adatoms. We argue that this sensitivity could be exploited to tailor the properties of magnetic devices by engineering the local environment and/or the operating conditions of nanomagnets.