Ground State Multiplicity Research Articles

Molecular Structural Formulas as One-Electron Density and Hamiltonian Operators: The VIF Method Extended

The valency interaction formula (VIF) method is given a broader and more general interpretation in which these simple molecular structural formulas implicitly include all overlaps between valence atomic orbitals even for interactions not drawn in the VIF picture. This applies for VIF pictures as one-electron Hamiltonian operators as well as VIF pictures as one-electron density operators that constitute a new implementation of the VIF method simpler in its application and more accurate in its results than previous approaches. A procedure for estimating elements of the effective charge density-bond order matrix, Pmunu, from electron configurations in atoms is presented, and it is shown how these lead to loop and line constants in the VIF picture. From these structural formulas, one finds the number of singly, doubly, and unoccupied molecular orbitals, as well as the number of molecular orbitals with energy lower, equal, and higher than -1/2Eh, the negative of the hydrogen atom's ionization energy. The VIF results for water are in qualitative agreement with MP2/6311++G3df3pd, MO energy levels where the simple VIF for water presented in the earlier literature does not agree with computed energy levels. The method presented here gives the simplest accurate VIF pictures for hydrocarbons. It is shown how VIF can be used to predict thermal barriers to chemical reactions. Insertion of singlet carbene into H2 is given as an example. VIF pictures as one-electron density operators describe the ground-state multiplicities of B2, N2, and O2 molecules and as one-electron Hamiltonian operators give the correct electronegativity trend across period two. Previous implementations of VIF do not indicate singly occupied molecular orbitals directly from the pictorial VIF rules for these examples. The direct comparison between structural formulas that represent electron density and those that represent energy is supported by comparison of a simple electronegativity scale, chiD=N/n2, with well-known electronegativity scales of Pauling, Mulliken, and Allen. This scale comes from the method used to calculate Pmumu for sp3 hybridized period-two elements and is comparable to electronegativity because it has the same form as <1/r> for hydrogenic orbitals. It therefore provides a physical basis for the representation of one electron density and Hamiltonian operators by the same VIF picture.

Tetrahedrane — Dossier of an Unknown

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Tetrahedrane—Dossier of an Unknown

To probe whether tetrahedrane should be isolable the thermodynamics and kinetics of C4H4 singlet and triplet structures were studied extensively at the CCSD(T)/cc-pVTZ//CCSD(T)/cc-pVDZ, CCSD(T)/cc-pVDZ, CCSD(T)/cc-pVDZ//B3 LYP/6-311G**, and B3 LYP/6-311G** levels of theory. The reaction of cyclopropene with atomic carbon, which was previously suggested to involve tetrahedrane as a reactive intermediate, was re-examined experimentally with low-temperature matrix-isolation techniques. While experimental and theoretical results exclude the intermediacy of tetrahedrane in the above reaction, it is predicted to be an isolable molecule. Among the many C4H4 species, we pay special attention to the electronic effects on the ground state multiplicity of the respective carbenes.

The Transfer of Tin and Germanium Atoms from N‐Heterocyclic Stannylenes and Germylenes to Diazadienes

New N-heterocyclic stannylenes and germylenes were synthesized by transamination of E[N(SiMe3)2] (E = Ge, Sn) with alpha-amino-aldimines or ethylidene-1,2-diamines and were characterized by spectroscopic methods and in the case of the germylene 10 g by X-ray diffraction. The reactions of several germylenes and stannylenes with diazadienes were studied by using dynamic NMR and computational methods. Experimental and theoretical studies confirmed that metathesis with exchange of the Group 14 atom is feasible for both stannylenes and germylenes, with exchange rates being generally higher for stannylenes. The metathesis of the diazadiene 3 b and the stannylene 1 b follows second-order kinetics and exhibits a sizeable negative entropy of activation. The transfer reaction is inhibited by bulky substituents in both reactants and surprisingly coincides with a suppression of the fragmentation of the stannylene into tin and diazadiene. A connection between oxidative addition and ring fragmentation was also observed in the reaction of 1 f with sulfur. Density functional theory (DFT) calculations suggest that all metathesis reactions proceed via transient spirocyclic [1+4] cycloaddition products, the formation of which is generally endothermic and endergonic. The spirostannanes display a distorted Psi-tbp geometry at the tin atom and their cycloreversion requires low or nearly negligible activation energies; spirogermanes exhibit distorted tetrahedral central atoms and sizeable energy barriers with respect to the same reaction. Complementary studies of cycloadditions of diazadienes to triplet germylenes or stannylenes indicate that these reactions are exothermic. The lowest triplet state in the carbene homologues results from promotion of an electron from an n(N) orbital with pi character rather than the n(C)-sigma orbital as in carbenes, and singlet-triplet excitation energies decrease from carbon to tin. Spirostannanes exhibit a triplet ground-state multiplicity that implies that the energy hypersurfaces for the reactions of singlet and triplet stannylenes with diazadienes intersect; for germylenes, the singlet hypersurface is always lower in energy. A reaction mechanism explaining the different thermal stabilities of N-heterocyclic germylenes and stannylenes, and the coincidence between ring metathesis and thermal decomposition of the latter, is proposed based on the different separation of the singlet and triplet energy hypersurfaces.

Charges of exceptionally twisted branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.

De novo prediction of the ground state structure of transition metal complexes using semiempirical and ab initio quantum mechanics. Coordination isomerism

The ground state coordination isomers for 30 different trigonal bipyramidal transition metal complexes have been predicted using different levels of quantum mechanics: semiempirical (PM3(tm)), ab initio (MP2//HF), pure (BPW91) and hybrid (B3PW91) density functional theory (DFT) methods. For species where these methods failed to reproduce crystallographic data, hybrid quantum mechanics/molecular mechanics (QM/MM) methods were used to study more exact experimental models. Literature deficiencies regarding ground state multiplicity of these species were supplemented by spin predictions using previously tested PM3(tm) methods. Geometry optimization calculations were performed for each possible coordination isomer. The predicted ground state minima provided by the different methods are compared to each other and with crystallographic data. Pure DFT functionals outperformed hybrid functionals and MP2//HF. The very rapid PM3(tm) parameterization method provided accurate predictions in comparison to other levels of theory. An integrated MM/PM3(tm)/DFT de novo scheme accurately reproduced crystallographic data for species where the individual methods failed.

Ground state multiplicity of acylnitrenes: computational and experimental studies

The singlet—triplet energy splitting (ΔE ST = E S − E T ) was calculated for formylnitrene (5) and for the syn- and anti-rotamers of carboxynitrene HOC(O)N (6) by the CCSD(T) method. Extrapolation of ΔE ST to a complete basis set was calculated to be negative for 5 and strongly positive for 6. Similar results were obtained by the G2 procedure. The reason for the dramatic stabilization of the singlet state appeared to be a special bonding interaction between the nitrogen and oxygen atoms, which results in the structure intermediate between those of nitrene and oxazirene. It was found that the B3LYP/6-31G(d) method overestimates ΔE ST by ∼9 kcal mol−1 for 5 and by ∼7 kcal mol−1 for 6. Taking into account this overestimation and the results of DFT calculations, it was concluded that benzoylnitrene has a singlet ground state. It was proved experimentally using photolysis of benzoyl azide in an argon matrix at 12 K that benzoylnitrene has a singlet ground state and its structure is similar to that of oxazirene. Nevertheless, these singlet intermediates have low barrier to the aziridine formation, which is traditionally considered to be a typical singlet nitrene reaction.

A DFT Study of the Ground State Multiplicities of Linear vs Angular Polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.

De novo prediction of ground state multiplicity and structural isomerism for transition metal complexes

Prediction of the ground state geometries and multiplicities for 33 transition metal tetrachlorides has been carried out using two different levels of quantum mechanics: semiempirical and density functional theory. All data regarding geometry and spin state provided by both computational methods were compared with experimental data when available. The calculations were performed for all possible spin multiplicities. The most important geometries for coordination number four (tetrahedral, square-planar, dodecahedral, and disphenoidal), as well as less symmetric structural isomers, were evaluated. A match between both computational methods in terms of predicted ground state multiplicity and geometry was found for 26 species, which translated into almost 80% agreement. Even though the PM3(tm) geometry prediction protocol involved more steps for isolating a feasible global minimum, the aggregate of these calculations was still orders of magnitude faster than DFT calculations using extended basis sets. The calculations indicate that caution is needed in the application of the PM3(tm) method to very high-spin transition metal complexes, but point to the suitability of very rapid semiempirical methods for reliable prediction of structural and ‘spin’ isomers, and hence their use in an efficient de novo design protocol for transition metal complexes.

The charges of a twisted brane

The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.

M-Phenylene-linked Bis-(biradicals): Generation, Characterization and Computational Studies

m-Phenylene-linked biscarbenes, bisnitrenes and carbenonitrenes can be formed photochemically from appropriate nitrogenous precursors. Generation of such reactive intermediates under matrix-isolation conditions allows for their characterization by spectroscopic techniques such as ESR, UV/vis and IR. The latter method is also useful in characterizing secondary products derived from these reactive intermediates. Computational chemistry methods complement experimental IR data, aiding, thus, in identification of such compounds. In addition electronic structure calculations help in developing qualitative and semi-quantitative models, which can be useful in predicting ground-state multiplicities. The parent systems of m-phenylene-linked carbenes and nitrenes have high-spin ground states, but a switching to lower multiplicity can be achieved by chemical substitution. The ground state and various low-lying excited states of m-phenylenecarbenonitrenes can be reasonably approximated by simple valence-bond depictions. Finally, m-phenylenecarbenonitrenes are photoreactive in the inert matrix isomerizing to cyclopropene derivatives.

Effects of Substitution on the Singlet−Triplet Energy Splittings and Ground-State Multiplicities of m-Phenylene-Based Diradicals: A Density Functional Theory Study

Unrestricted density functional calculations with spin-projection procedures have been performed for a series of m-phenylene-bridged diradicals to investigate the effects of substitution on the singlet−triplet (S−T) energy gaps and the ground-state multiplicities. Our calculations show that the introduction of electron-donating (or electron-withdrawing) substituents on 4,6-positions of the m-phenylene moiety or on the radical centers, or on both positions, generally leads to a triplet ground state, although the S−T energy gaps are smaller than that of the parent m-xylylene diradical to some extent. However, the simultaneous substitution of electron-donating and electron-withdrawing groups at m-phenylene and radical centers, and vice versa, will result in a singlet ground state or a very small positive S−T gap. A perturbative analysis based on the SOMO−SOMO energy splittings, the spatial distributions of SOMOs, and the population of the spin densities calculated for the triplet state has been presented to elucidate factors determining the S−T gap and ground-state multiplicity in studied diradicals.

Spin-forbidden deprotonation of aqueous nitroxyl (HNO).

The first mechanistic study of a spin-forbidden proton-transfer reaction in aqueous solution is reported. Laser flash photolysis of alkaline trioxodinitrate (N(2)O(3)(2)(-), Angeli's anion) is used to generate a nitroxyl anion in its excited singlet state ((1)NO(-)). Through rapid partitioning between protonation by water and electronic relaxation, (1)NO(-) produces (1)HNO (ground state, yield 96%) and (3)NO(-) (ground state, yield 4%), which comprise a unique conjugate acid-base couple with different ground-state multiplicities. Using the large difference between reactivities of (1)HNO and (3)NO(-) in the peroxynitrite-forming reaction with (3)O(2), the kinetics of spin-forbidden deprotonation reaction (1)HNO + OH(-) --> (3)NO(-) + H(2)O is investigated in H(2)O and D(2)O. Consistent with proton transfer, this reaction exhibits primary kinetic hydrogen isotope effect k(H)/k(D) = 3.1 at 298 K, which is found to be temperature-dependent. Arrhenius pre-exponential factors and activation energies of the second-order rate constant are found to be: log(A, M(-)(1) s(-)(1)) = 10.0 +/- 0.2 and E(a) = 30.0 +/- 1.1 kJ/mol for proton transfer and log(A, M(-)(1) s(-)(1)) = 10.4 +/- 0.1 and E(a) = 35.1 +/- 0.7 kJ/mol for deuteron transfer. Collectively, these data are interpreted to show that the nuclear reorganization requirements arising from the spin prohibition necessitate significant activation before spin change can take place, but the spin change itself must occur extremely rapidly. It is concluded that a synergy between the spin prohibition and the reaction energetics creates an intersystem barrier and is responsible for slowness of the spin-forbidden deprotonation of (1)HNO by OH(-); the spin prohibition alone plays a minor role.

Assertion and validation of the performance of the B3LYP⋆ functional for the first transition metal row and the G2 test set

The exact exchange part in hybrid density functionals is analyzed with respect to the prediction of ground state multiplicities. It has been found [M. Reiher, O. Salomon, and B. A. Hess, Theor. Chem. Acc., 107, 48 (2001)] that pure and hybrid density functionals yield energy splittings between high-spin and low-spin states of Fe–sulfur complexes that differ by more than 100 kJ/mol and thus fail to reliably predict the correct multiplicity of the ground state. This deviation can lead to meaningless reaction energetics for metal-catalyzed reactions. The finding that the energy splitting depends linearly on the exact exchange admixture parameter led to a new parametrization of the B3LYP functional which was dubbed B3LYP⋆. In the present paper we investigate the generality and transferability of this functional. We study the extent to which the exact exchange admixture affects the thermochemistry validated with respect to the reference data set of molecules from the G2 test set. Metallocenes and bis(benzene) metal complexes of the first transition metal period are chosen to test the transferability of the findings for Fe–sulfur complexes. Moreover, the slope of the linear dependence of the energy splitting of high-spin and low-spin states on the amount of admixture of exact exchange is studied in detail.

Halogen derivatives of m-phenylene(carbeno)nitrene: a switch in ground-state multiplicity.

m-Phenylene-coupled carbenonitrenes [(3-nitrenophenyl)methylene (2-H), (3-nitrenophenyl)fluoromethylene (2-F), (3-nitrenophenyl)chloromethylene (2-Cl), (3-nitrenophenyl)bromomethylene (2-Br)] have been investigated computationally (with B3LYP, MCSCF, CASPT2, ROMP2, and QCISD(T) methods) and experimentally (with IR, UV, and ESR spectroscopy). For each species, five electronic states were considered. At the highest level of theory explored, the parent compound (2-H) has a quintet ground state, but its halogen derivatives (2-X, X = F, Cl, and Br) have triplet ground states. A linear relationship between the Q[bond]T energy gap of 2-X and the T-S gap of the corresponding phenylcarbenes 8-X is found, which can be helpful in rationalizing and predicting ground-state multiplicities in m-phenylene-linked carbenonitrenes and similar species. Precursors for the photochemical generation of 2-X (X = H, F, Cl, and Br) were synthesized and photolyzed in matrixes (Ar, triacetin) at low temperatures. IR (Ar, 13 K) and ESR (triacetin, 77 K) data are compatible with the generation of triplet halocarbenonitrenes 2-X, (X = F, Cl, and Br). All four compounds upon further irradiation undergo isomerization to substituted cyclopropenes 5-X (X = H, F, Cl, and Br), as suggested by their IR spectra.

Acid−Base-Driven Multilevel Switching of Electronic Coupling in 2,4-Dimethylene Five-Member Heterocycles

The ground state multiplicity of 2,4-dimethylene five-member heterocycles is dependent on the protonation of the heteroatom. The relative singlet and triplet energy at π-CASSCF-optimized geometries varies and is dependent on the number of protons attached to the heteroatom. The 2,4-dimethylenecyclopentadiene anion (X = CH-) and the 2,4-dimethylenepyrrole anion (X = N-) are ground state singlets while the 2,4-dimethylenecyclopentadiene (X = CH2) and 2,4-dimethylenepyrrole cation (X = NH2+) are ground state triplets. The neutral 2,4-dimethylenepyrrole (X = NH) is a ground state triplet with a weaker preference than that calculated for the 2,4-dimethylenepyrrole cation. Similarly, the protonated 2,4-dimethylenefurane (X = OH+) is a strongly preferred ground state triplet while the neutral 2,4-dimethylenefurane (X = OH) has a weaker preference for the triplet ground state. Analogous relationships exist for the systems with the third-row elements. These properties of the 2,4-dimethylene five-member heterocycle...

Isolation of the Phenyl Cation in a Solid Argon Matrix

Vacuum UV photolysis of halobenzenes 1 results in the formation of the phenyl cation (2), which is isolated in solid argon matrices. The structure and ground-state multiplicity of 2 were unequivocally determined by IR spectroscopy in combination with isotopic labeling experiments and comparisons with DFT calculations. Furthermore, 2 can be captured by N2 to form the benzene diazonium ion.

Ground-state multiplicities of atoms and positive ions

A procedure is developed to establish the ground-state multiplicities for atoms with any number of electrons. The procedure is applied to two- and three-electron systems. The results are that all neutral and positive two- and three-electron atoms have singlet (S=0) and doublet (S=1/2) ground states, respectively.

2D-Electron Spin Transient Nutation (2D-ESTN) Study of a Stable High- Spin Carbene (S=3)

Stable high-spin polycarbene, polybrominated 1,3,5-tris[4-(phenylcarbeno)-phenylethy-nyl]benzene in a glass matrix was studied by Electron Spin Transient Nutation (ESTN) spectroscopy. 2D-ESTN spectra of the polycarbene were measured in order to identify a molecular spin multiplicity of the high-spin ground state. The observed nutation frequencies were assigned to those arising from the allowed ESR transitions of the septet ground state (S=3). It indicates that the high-spin state is generated by ferromagnetic interaction between stable bromo-substituted diphenylmethylenes (S=1) through a 2D topological spin coupling unit with C 3 symmetry, 1,3,5-tris(ethynyl)benzene. The observed fine-structure parameters of the septet state, D = −0.040 cm −1 and |E| = 0.007 cm −1, were well interpreted in terms of an intramolecular spin-spin interaction model. The observed small and negative D value was shown to arise from the C 3 symmetric molecular structure. The high-spin polycarbene has survived after annealing of the glass matrix. The stable triplet carbene unit is supposed to serve as a useful building block for extended super high-spin molecular systems and organic superparamagnets.

On the Ground State Multiplicity of Donor-Substituted Cyclopentadienyl Cations

It is shown that amino-substituted cyclopentadienyl cations (CPC) and benz-annelated amino CPCs might form a triplet ground state at torsion of the amino group out of the plane of the anti-aromatic CPC ring.