Spin Multiplicity Research Articles

Probing the structural and electronic properties of aluminum-sulfur Al n S m (2 ≤ n + m ≤ 6) clusters and their oxides

Using the first-principle density functional calculations, the equilibrium geometries and electronic properties of anionic and neutral aluminum-sulfur AlnSm (2≤n+m≤6) clusters have been systematically investigated at B3PW91 level. The optimized results indicate that the lowest-energy structures of the anionic and neutral AlnSm clusters prefer the low spin multiplicities (singlet or doublet) except the Al2‾, Al2, S2, Al4 and Al2S4 clusters. A significant odd-even oscillation of the highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps for the AlnSm‾ clusters is observed. Electron detachment energies (both vertical and adiabatic) are discussed and compared with the photoelectron spectra observations. Furthermore, a good agreement between experimental and theoretical results gives confidence in the most stable clusters considered in the present study and validates the chosen computational method. In addition, the variation trend of chemical hardness is in keeping with that of HOMO-LUMO energy gaps for the AlnSm clusters. Upon the interaction of oxygen with the stable AlSm‾ clusters, the dissociative chemisorptions are favorable in energy. The binding energy and Gibbs free energy change show completely opposite oscillating behaviors as the cluster size increases.

Spin Multiplicity and Symmetry Breaking in Vanadium-Benzene Complexes

We present accurate quantum Monte Carlo (QMC) calculations which enabled us to determine the structure, spin multiplicity, ionization energy, dissociation energy, and spin-dependent electronic gaps of the vanadium-benzene system. From total and ionization energy we deduce a high-spin state with vastly different energy gaps for the two spin channels. For this purpose we have used a multistage combination of techniques with consecutive elimination of systematic biases except for the fixed-node approximation in QMC calculations. Our results significantly differ from the established picture based on previous less accurate calculations and point out the importance of high-level many-body methods for predictive calculations of similar transition metal-based organometallic systems.

How Can f‐Block Monocations Behave as Monocations of d‐Block Transition Metals?

AbstractThe electronic structures of LnNH+ species are studied by DFT (B3LYP) quantum calculations for the Ln = La, Eu and Gd 4f‐block elements (lanthanides). Ln≡N triple bonds of essentially d character are formed for La and Gd, which explains why La+ and Gd+ behave like ions of d‐block transition metals, as experimentally evidenced by mass spectrometry, and why the Ln+ reactivity is correlated with its electron‐promotion energy: the present theoretical study is a support to such a correlation and qualitative knowledge. The Ln+ + NH3 → LnNH3+ → transition state → HLn=NH2+ → transition state → Ln≡NH+ + H2 reaction pathway is calculated. The formation of H–Ln=NH2+ corresponds to the formation of new covalent bonds associated with more electron pairing and corresponding lowering of the spin multiplicity–spin crossing reaction. It is in this step that low electron‐promotion energy is required to promote a 4f electron into a 5d orbital as is typical for La+ and Gd+. A similar geometry, bonding and electronic configuration are calculated for NpNH+ – an actinide complex observed by mass spectrometry – with higher participation of 5f orbitals (20 % and 25 % for the σ and π bonds, respectively) as compared to the 4f orbitals (3 % and 8 %) of GdNH+: Gd+ and Np+ are the only lanthanide and actinide monocations with one s‐ and one d‐valence electrons in their ground states.

Extensive Computational Study on Coordination of Transition Metal Cations and Water Molecules to Glutamic Acid

On the basis of the conformations of glutamic acid (Glu) and analysis of possible metal cation coordination and hydration modes, conformations of Glu metalated with transition metal cations (TMCs), Cu(+/2+), Zn(+/2+), and Fe(+/2+/3+) and hydrations of Glu-Cu(+/2+) and Glu-Zn(+/2+) complexes by up to three water molecules are determined by extensive computational searches. The BHandHLYP functional is chosen as the main computational method as its overall performance for treating the spin multiplicity of TMCs is similar to that of CCSD(T) and better than that of MP2 and B3LYP. All mono- and divalent TMCs prefer tridentate coordination to canonical Glu, while Fe(3+) favors a bidentate coordination to zwitterionic Glu. The ground state of Glu-Fe(+) is found to be a spin sextet. Metal ion affinities of Glu for the TMCs are determined, and an excellent agreement with the experiment for Cu(+) may be obtained if the entropic effect is properly accounted for. Effects of hydration on the stabilities of different Glu-Cu(+/2+)/Zn(+/2+) structures are discussed, and the hydration energies for up to three water molecules are obtained. For the global minimum to take the zwitterionic form, Glu-Zn(+) requires only monohydration, Glu-Zn(2+) needs to be trihydrated, while Glu-Cu(+/2) should be hydrated with four or more water molecules.

Excitonic properties of armchair graphene nanoribbons from exact diagonalization of the Hubbard model

We report on excitonic spectra of armchair graphene nanoribbons (AGNRs) obtained from a full many-body exact diagonalization of the Hubbard model within low and intermediate correlation regimes and with a complete characterization of the spin multiplicity of the calculated eigenstates. Our results allow us to group these systems into three different families according to the sequence of the one- and two-photon allowed states and the magnitude of the respective optical oscillator strengths within the investigated correlation regime. The oscillator strengths for the one-photon allowed transitions are found to be lower than those obtained previously for zigzag semiconducting single-walled carbon nanotubes, pointing out a qualitatively different photophysical behaviour of AGNRs.

A novel relationship between the radical-scavenging activity of flavonoids and enthalpy of formation revealed with Hartree–Fock computations and thermochemical deduction

ObjectiveThe present study aims to establish the relationship between the reported radical-scavenging activities of flavonoids and some enthalpy changes that may occur during flavonoids' reactions with free radicals.MethodEight flavonoids were chosen for the study on the basis of their structural merits and reported 1,1-diphenyl-2-picryl-hydrazyl scavenging activities. Enthalpy changes accompanying interconversions between selected conformations (including spin multiplicities) and homolytic dissociations were estimated.ResultsA novel relationship exists between the total enthalpy of reaction for the abstraction of two hydrogen atoms from flavonoids, their reported radical-scavenging activities and the enthalpy of the homolytic dissociation of hydrogen molecule (104.206 kcal mol−1). Only those flavonoids which could give up two hydrogen atoms with total enthalpy changes well below 104.206 kcal mol−1 were active radical scavengers.DiscussionBy appealing to equilibrium dynamics, we demonstrated that, for flavonoids to be able to donate hydrogen atoms, the change in enthalpy accompanying the abstraction of two hydrogen atoms needs to be less than 104.206 kcal mol−1. This condition does not seem to be restricted to flavonoids only but rather generally applicable to chian-breaking antioxidants.ConclusionThermodynamical relationships may be the most important factors governing the radical-scavenging reactions of flavonoids and possibly other compounds as well. Nevertheless, a more complete characterization of antioxidants would necessitate kinetic analysis.

Shape of polygonal quantum dots and ground-state instability in the spin polarization

We theoretically investigate the ground-state electronic structure and the spin polarization of four electrons confined in two-dimensional (2D) polygonal quantum dots. We employ standard mean-field theory approaches using unrestricted Hartree--Fock (UHF) and density functional theory (DFT) calculations. Resonant UHF configuration interaction (res-UHF CI) calculations were also performed to incorporate the electron correlation more intuitively. Odd polygons (trigons and pentagons) preferentially generate the ground-state triplet as predicted by Hund's rule, whereas even polygons (tetragons, hexagons, and octagons) promote ground-state instability in the spin multiplicity and tend to produce an anti-Hund state of the ground-state singlet with strengthening of the interelectron interaction. The circle, a limited polygon having an infinite number of apexes, divides these odd and even polygons, and the ground-state instability can be well classified by the area of the polygon apexes that protrudes from an equisized circle.

Magnetic structure variation in manganese-oxide clusters

Negative-ion photoelectron spectroscopy and ab initio simulations are used to study the variation in magnetic structure in Mn(x)O(y) (x = 3, 4[semicolon] y = 1, 2) clusters. The ferrimagnetic and antiferromagnetic ground-state structures of Mn(x)O(y) are 0.16-1.20 eV lower in energy than their ferromagnetic isomers. The presence of oxygen thus stabilizes low-spin isomers relative to the preferred high-spin ordering of bare Mn(3) and Mn(4). Each cluster has a preferred overall magnetic moment, and no evidence is seen of competing states with different spin multiplicities. However, non-degenerate isomags, which possess the same spin multiplicity but different arrangements of local moments, do contribute additional features and peak broadening in the photoelectron spectra. Proper accounting for all possible isomags is shown to be critical for accurate computational prediction of the spectra.

Pseudo Jahn-Teller Origin of Perovskite Multiferroics, Magnetic-Ferroelectric Crossover, and Magnetoelectric Effects: Thed0−d10Problem

The conditions of multiferroicity in d(n) perovskites are derived from the pseudo Jahn-Teller effect, due to which ferroelectric displacements are triggered by vibronic coupling between ground and excited electronic states of opposite parity but same spin multiplicity; it takes place for some specific d(n) configurations and spin states only. In combination with the high-spin-low-spin crossover effect this leads to a novel phenomenon, the magnetic-ferroelectric (multiferroics) crossover which predicts magnetoelectric effects with exciting functionalities including electric magnetization and demagnetization.

Discovery of Magnetic Superatoms and Assessment of van der Waals Dispersion Effects in Csn Clusters

We report the global minimum (GM) structures and electronic properties of Csn clusters with up to 80 atoms, obtained employing a density functional theory method which accounts for van der Waals dispersion interactions (vdW-DFT). The GM structures of Csn are found to differ markedly from those of lighter alkali clusters like Nan. Three main physical factors are invoked to interpret the differences: vdW attraction, sd hybridization, and spin polarization. vdW effects are found to modify the GM structures of many Csn clusters as compared to the predictions of local and semilocal DFT approximations and tend to favor compact structures. sd hybridization accounts for the enhanced stability of strained motifs such as icosahedra or Kasper polyhedra. Finally, spin polarization stabilizes highly symmetric structures with a high orbital degeneracy. The electric dipole moments of most Csn clusters are close to zero, a distinguishing feature of metallicity previously observed for Nan clusters. However, our predictions show that some clusters like Cs10 or Cs26 have sizable electric dipole moments. High spin multiplicities are observed for many different sizes. The spontaneous magnetization of pure Csn clusters is intrinsic and exclusively due to delocalized electrons. This allows us to extend the concept of superatoms (multicenter systems that mimic the electronic behavior of elemental atoms) so that it encompasses also magnetic properties, without the need to introduce localized electrons or extrinsic impurities. The physical reasons for the stability of magnetic superatoms are identified and described.

Spin and elastic contributions to isothermal entropy change

Statistical considerations of ensembles of localized magnetic moments reveal an upper bound of the isothermal entropy change when only the magnetic degrees of freedom are considered. In this case, the maximum molar isothermal entropy change is determined by the spin multiplicity and is equal to Rln(2J + 1), where J is the angular momentum of an individual atom. However, in materials with giant magnetocaloric effect, the isothermal field-induced entropy change goes beyond the spin-multiplicity limit due to field-activated elastic degrees of freedom. Recently, we investigated a model of pairs of exchange-coupled Ising spins with variable real-space positions. We showed, within a classical approximation for the elastic degree of freedom, that a vibrational entropy contribution can be activated via applied magnetic fields. Here we quantify the impact of quantum corrections in the low-temperature limit. We compare calculations that include elastic interaction with the rigid exchange model in the high-temperature limit. We find that quantum effects provide quantitative corrections in the low-temperature limit. In addition we show that the elastic contributions to the isothermal entropy change can be additive but, remarkably, it can also give rise to reduced isothermal entropy change in certain temperature regions.

A two‐state reactivity rationale for the reaction of ta atom with acetonitrile in the gas phase

AbstractThe spin‐forbidden reaction mechanism of Ta (4F, 5d36s2) with CH3CN, on two different potential surfaces (PESs) has been investigated at the B3LYP, MP2, and CCSD level of theory. Crossing points between the PESs are located using different methods, and possible spin inversion processes are discussed by means of spin‐orbit coupling calculations. As a result, the reaction system will change its spin multiplicities near this crossing seam, leading to a significant decrease in the barrier of 2‐4TS3 from 24.17 to 5.36 kcal/mol, which makes the reaction access to a lower energy pathway and accelerate the reaction rate. © 2012 Wiley Periodicals, Inc.

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.

Theoretical Study of Inverted Sandwich Type Complexes of 4d Transition Metal Elements: Interesting Similarities to and Differences from 3d Transition Metal Complexes

Inverted sandwich type complexes (ISTCs) of 4d metals, (μ-η(6):η(6)-C(6)H(6))[M(DDP)](2) (DDPH = 2-{(2,6-diisopropylphenyl)amino}-4-{(2,6-diisopropylphenyl)imino}pent-2-ene; M = Y, Zr, Nb, Mo, and Tc), were investigated with density functional theory (DFT) and MRMP2 methods, where a model ligand AIP (AIPH = (Z)-1-amino-3-imino-prop-1-ene) was mainly employed. When going to Nb (group V) from Y (group III) in the periodic table, the spin multiplicity of the ground state increases in the order singlet, triplet, and quintet for M = Y, Zr, and Nb, respectively, like 3d ISTCs reported recently. This is interpreted with orbital diagram and number of d electrons. However, the spin multiplicity decreases to either singlet or triplet in ISTC of Mo (group VI) and to triplet in ISTC of Tc (group VII), where MRMP2 method is employed because the DFT method is not useful here. These spin multiplicities are much lower than the septet of ISTC of Cr and the nonet of that of Mn. When going from 3d to 4d, the position providing the maximum spin multiplicity shifts to group V from group VII. These differences arise from the size of the 4d orbital. Because of the larger size of the 4d orbital, the energy splitting between two d(δ) orbitals of M(AIP) and that between the d(δ) and d(π) orbitals are larger in the 4d complex than in the 3d complex. Thus, when occupation on the d(δ) orbital starts, the low spin state becomes ground state, which occurs at group VI. Hence, the ISTC of Nb (group V) exhibits the maximum spin multiplicity.

Periodic tables of diatomic and triatomic molecules

The Mendeleev periodic table of atoms is one of the most important principles in natural science. However, there is shortage of analog for molecules. Here we propose two periodic tables, one for diatomic molecules and one for triatomic molecules. The form of the molecular periodic tables is analogous to that of Mendeleev periodic table of atoms. In the table, molecules are classified and arranged by their group number G, which is the number of valence electrons, and the periodic number P, which represents the size of the molecules. The basic molecular properties, including bond length, binding energy, force constant, ionization potential, spin multiplicity, chemical reactivity, and bond angle, change periodically within the tables. The periodicities of diatomic and triatomic molecules are thus revealed. We also demonstrate that the periodicity originates from the shell-like electronic configurations of the molecules. The periodic tables not only contain free molecules, but also the “virtual” molecules present in polyatomic molecules. The periodic tables can be used to classify molecules, to predict unknown molecular properties, to understand the role of virtual molecules in polyatomic molecules, and to initiate new research fields, such as the periodicities of aromatic species, clusters, or nanoparticles. The tables should be of interest not only to scientists in a variety of disciplines, but also to undergraduates studying natural sciences.

Theoretical Studies of the Excited Doublet States of SF and SCl and Singlet States of SF2, SFCl, and SCl2

In previous work, we reported that the lowest-lying excited states of SF, SCl, SF(2), SFCl, and SCl(2) have recoupled pair bonds. In this study, we examine the analogous low-spin states--the (2)Σ(-) and (2)Δ states of SF and SCl and the excited singlet states of SF(2), SCl(2), and SFCl--which also possess recoupled pair bonds. In contrast to the excited states treated previously, the states studied in the present work have the same spin multiplicities as their respective ground states and are thus potentially observable via electronic excitation. Of particular interest are the minima on the (1)A″ potential energy surface of SFCl corresponding to bond-stretch isomers analogous to those found on the (3)A″ surface. In addition, we discovered that the first two excited states ((1)A″) accessible via vertical excitations from the ground state of SFCl have the electronic structure of the bond-stretch isomers. Thus, electronic excitation spectroscopic studies of SFCl could reveal a signature of the bond-stretch isomers. We will also present limited data on the lowest singlet Rydberg states of the triatomic species. Calculations were performed at the MRCI+Q/aug-cc-pV(Q+d,5+d)Z levels of theory.

A spin-adapted size-extensive state-specific multi-reference perturbation theory with various partitioning schemes. II. Molecular applications

Following the theoretical development of a spin-adapted state-specific multi-reference second-order perturbation theory (SA-SSMRPT2) as expounded in the preceding publication, we discuss here its implementation and the results of its applications to potential energy curves (PECs) of various electronic states of small molecules. In particular, we illustrate its efficacy in states of various spin multiplicities and varying multi-reference character. Both Møller-Plesset (MP) and Epstein-Nesbet (EN) type of partitions have been explored. Also, a straightforward Rayleigh-Schrödinger (RS) and Brillouin-Wigner (BW) version of the SA-SSMRPT2 have been studied. Ground state PECs were computed for singlet states of HF, BH, and H(2)O molecules as well as the doublet state of NH(2) and BeH radicals and compared to corresponding full configuration interaction numbers, which serve as benchmark results. As an extensive application on a production level, the ground state PECs of N(2), a classic example of multiple-bond breaking, were calculated using cc-pVXZ (X = 3,4,5) basis and then extrapolated to obtain estimates of the complete basis set limit. Vibrational energy levels were extracted from these N(2) PECs, which compare favorably to the experimental values. In addition, extensive studies were also carried out on PECs of the seven low-lying excited states of the N(2) molecule. Finally, it is shown that the flexibility to relax configuration coefficients in SA-SSMRPT2 helps to provide good descriptions for the avoided crossing between the two lowest (1)Σ states of the LiF molecule. Our results indicate (1) that more studies are needed to draw firm conclusions about the relative efficacies of the MP and EN results and (2) that the RS version works so well as compared to the BW version that the extra computational expenses needed in the later formalism is not warranted.

Electronic States and Metal–Ligand Bonding of Gadolinium Complexes of Benzene and Cyclooctatetraene

Gadolinium (Gd) complexes of benzene (C(6)H(6)) and (1,3,5,7-cyclooctatetraene) (C(8)H(8)) were produced in a laser-vaporization supersonic molecular beam source and studied by single-photon pulsed-field ionization zero electron kinetic energy (ZEKE) spectroscopy. Adiabatic ionization energies and metal-ligand stretching frequencies were measured for the first time from the ZEKE spectra. Metal-ligand bonding and electronic states of the neutral and cationic complexes were analyzed by combining the spectroscopic measurements with ab initio calculations. The ground states of Gd(C(6)H(6)) and [Gd(C(6)H(6))](+) were determined as (11)A(2) and (10)A(2), respectively, with C(6v) molecular symmetry. The ground states of Gd(C(8)H(8)) and [Gd(C(8)H(8))](+) were identified as (9)A(2) and (8)A(2), respectively, with C(8v) molecular symmetry. Although the metal-ligand bonding in Gd(C(6)H(6)) is dominated by the covalent interaction, the bonding in Gd(C(8)H(8)) is largely electrostatic. The bonding in the benzene complex is much weaker than that in the cyclooctatetraene species. The strong bonding in Gd(C(8)H(8)) arises from two-electron transfer from Gd to C(8)H(8), which creates a strong charge-charge interaction and converts the tub-shaped ligand into a planar form. In both systems, Gd 4f orbitals are localized and play little role in the bonding, but they contribute to the high electron spin multiplicities.

Theoretical study of spin-orbit coupling and intersystem crossing in the two-state reaction between Nb(NH2)3 and N2O

The two-state mechanism of the reaction of Nb(NH2)3 with N2O on the singlet and triplet potential energy surfaces has been investigated at the B3LYP level. Crossing points between the potential energy surfaces have been located using different methods. Analysis of the strain model shows that the singlet state of the four-coordinate (N2O)Nb(NH2)3 complex with N2O bonded via terminal N atom coordination (12) is more stable in the initial stage of reaction, since the bending of the N2O fragment [Edef(N2O) = 86.1 kcal mol−1] results in an energy splitting of the doubly degenerate LUMO; the low-energy LUMO can now strongly couple with the occupied Nb-localized d orbitals, forming a back-bond and transferring charge (q = 0.82 e) from Nb(NH2)3 to the N2O ligand. Going from 32 to 12, the reacting system changes spin multiplicity near the MECP (minimal energy crossing point) region, which takes place with a spin crossing barrier of 9.6–10.0 kcal mol−1. Analysis of spin-orbit coupling (SOC) indicates that MECP will produce a significant SOC matrix element. The value of SOC is 111.52 cm−1, due to the electron shift between two perpendicular ϕ orbitals with the same rotation direction, and the magnitude of the spin-multi-plicity mixing increases in the small energy gap between high- and low-spin states, greatly enhancing the probability of intersystem crossing. The probabilities of single (P1ISC) and double (P2ISC) passes estimated at MECP (SOC = 111.52 cm−1) are approximately 1.17×10−2 and 2.32×10−2, respectively.

A theoretical study of closed polyacene structures

The electronic structure of planar molecular edifices obtained by joining polyacene fragments (polyacene stripes) is investigated at tight-binding and ab initio levels. It is shown that the presence of 60° angles in the molecular skeleton induces the formation of singly-occupied molecular orbitals, whose combination gives rise to quasi-degenerate electronic states. The ab initio investigation requires therefore the use of CAS-SCF and MR-PT approaches. The three types of possible convex polygons having a unique side length (hexagons, rhombuses and triangles) have been considered in this work. The spin multiplicity of these quasi-flat molecular structures is found to be in systematical accord with the Ovchinnikov rule.