Interpretation of Hund's multiplicity rule for the carbon atom

Hund's multiplicity rule is investigated for the carbon atom using quantum Monte Carlo methods. Our calculations give an accurate account of electronic correlation and obey the virial theorem to high accuracy. This allows us to obtain accurate values for each of the energy terms and therefore to give a convincing explanation of the mechanism by which Hund's rule operates in carbon. We find that the energy gain in the triplet with respect to the singlet state is due to the greater electron-nucleus attraction in the higher spin state, in accordance with Hartree-Fock calculations and studies including correlation. The method used here can easily be extended to heavier atoms.     

Violation of Hund's rule in the lowest excited singlet-triplet pairs of dicyclohepta[cd,gh]pentalene and dicyclopenta[ef,kl]heptalene

Using the Pariser-Parr-Pople type MO method, the energy ordering of the lowest excited singlet-triplet pairs of the title molecules is examined by taking into account ample configuration interactions. In dicyclohepta[cd,gh]pentalene, it is shown that the lowest excited singlet state lies below the corresponding triplet state by about 6 kcal/mol. This violation of Hund's rule is ascribed entirely to the correlation effects brought about by spin polarization terms. Such a violation of Hund's rule is expected to occur in the lowest excited states of dicyclopenta[ef,kl]heptalene.     

Nonadiabatic molecular dynamics simulations of correlated electrons in solution. 1. Full configuration interaction (CI) excited-state relaxation dynamics of hydrated dielectrons

The hydrated dielectron is composed of two excess electrons dissolved in liquid water that occupy a single cavity; in both its singlet and triplet spin states there is a significant exchange interaction so the two electrons cannot be considered to be independent. In this paper and the following paper,we present the results of mixed quantum/classical molecular dynamics simulations of the nonadiabatic relaxation dynamics of photoexcited hydrated dielectrons, where we use full configuration interaction (CI) to solve for the two-electron wave function at every simulation time step. To the best of our knowledge, this represents the first systematic treatment of excited-state solvation dynamics where the multiple-electron problem is solved exactly. The simulations show that the effects of exchange and correlation contribute significantly to the relaxation dynamics. For example, spin-singlet dielectrons relax to the ground state on a time scale similar to that of single electrons excited at the same energy, but spin-triplet dielectrons relax much faster. The difference in relaxation dynamics is caused by exchange and correlation: The Pauli exclusion principle imposes very different electronic structure when the electrons' spins are singlet paired than when they are triplet paired, altering the available nonadiabatic relaxation pathways. In addition, we monitor how electronic correlation changes dynamically during nonadiabatic relaxation and show that solvent dynamics cause electron correlation to evolve quite differently for singlet and triplet dielectrons. Despite such differences, our calculations show that both spin states are stable to excited-state dissociation, but that the excited-state stability has different origins for the two spin states. For singlet dielectrons, the stability depends on whether the solvent structure can rearrange to create a second cavity before the ground state is reached. For triplet dielectrons, in contrast, electronic correlation ensures that the two electrons do not dissociate, even if the dielectron is artificially kept from reaching the ground state. In addition, both singlet and triplet dielectrons change shape dramatically during relaxation, so that linear response fails to describe the solvation dynamics for either spin state. In the following paper (Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2006, 110, 9692), we use these simulations to calculate the pump-probe spectroscopic signal expected for photoexcited hydrated dielectrons and to predict an experiment to observe hydrated dielectrons directly.     

Hartree–Fock instabilities and electronic properties

Hartree–Fock instabilities are investigated for about 80 compounds, from acetylene to mivazerol (27 atoms) and a cluster of 18 water molecules, within a double ζ basis set. For most conjugated systems, the restricted Hartree–Fock wave function of the singlet fundamental state presents an external or so‐called triplet instability. This behavior is studied in relation with the electronic correlation, the vicinity of the triplet and singlet excited states, the electronic delocalization linked with resonance, the nature of eventual heteroatoms, and the size of the systems. The case of antiaromatic systems is different, because they may present a very large internal Hartree–Fock instability. Furthermore, the violation of Hund's rule, observed for these compounds, is put in relation with the fact that the high symmetry structure in its singlet state has no feature of a diradical‐like species. It appears that the triplet Hartree–Fock instability is directly related with the spin properties of nonnull orbital angular momentum electronic systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 483–504, 2000     

Electron correlation and Hund's rule

It is suggested that simple electronic shielding effects induced by wave function antisymmetrization tend to govern the energy ordering of singlet and triplet terms within a two-electron atomic configuration. This approach gives rise to the following alternating rule: For the term of greatest orbital angular momentum within a configuration, the triplet lies below the singlet. The energy ordering reverses for the term of next highest angular momentum, and continues to alternate with each change of one unit in the orbital angular momentum until the term of lowest angular momentum is reached. In an examination of over 600 energy levels of the elements and their ions, the alternating rule reliably orders singlet–triplet energy levels in some 90% of the cases.     

Theoretical study of some bis-verdazyl diradicals: singlet–triplet energy gap

The bis-verdazyl diradical (BVD) system is closely examined by using the multiconfiguration wavefunctions as well as the density functional theory (DFT). The totally symmetric singlet ground state turns out to have strong multiconfiguration character at all levels of theory. The singlet ground state takes on the planar structure while the most stable triplet state corresponds to the twisted form. The MCSCF+MCQDPT2 calculations are shown to be sufficient to predict the singlet–triplet energy gap which is insensitive to the electronic characters of the ring substituents.     

Unimolecular decomposition of chemically activated pentatetraene (H2CCCCCH2) intermediates: A crossed beams study of dicarbon molecule reactions with allene

The reactions dynamics of the dicarbon molecule C2 in the 1Sigma (g)+ singlet ground state and 3Pi(u) first excited triplet state with allene, H2CCCH2(X1A1), was investigated under single collision conditions using the crossed molecular beam approach at four collision energies between 13.6 and 49.4 kJ mol(-1). The experiments were combined with ab initio electronic structure calculations of the relevant stationary points on the singlet and triplet potential energy surfaces. Our investigations imply that the reactions are barrier-less and indirect on both the singlet and the triplet surfaces and proceed through bound C5H4 intermediates via addition of the dicarbon molecule to the carbon-carbon double bond (singlet surface) and to the terminal as well as central carbon atoms of the allene molecule (triplet surface). The initial collision complexes isomerize to form triplet and singlet pentatetraene intermediates (H2CCCCCH2) that decompose via atomic hydrogen loss to yield the 2,4-pentadiynyl-1 radical, HCCCCCH2(X2B1). These channels result in symmetric center-of-mass angular distributions. On the triplet surface, a second channel involves the existence of a nonsymmetric reaction intermediate (HCCCH2CCH) that fragments through atomic hydrogen emission to the 1,4-pentadiynyl-3 radical [C5H3(X2B1)HCCCHCCH]; this pathway was found to account for the backward scattered center-of-mass angular distributions at higher collision energies. The identification of two resonance-stabilized free C5H3 radicals (i.e., 2,4-pentadiynyl-1 and 1,4-pentadiynyl-3) suggests that these molecules can be important transient species in combustion flames and in the chemical evolution of the interstellar medium.     

Influence of electron correlation on the character of the splitting of degenerate states in metalloporphyrin dianions

The lowest singlet and triplet energy levels of metalloporphyrin dianions have been calculated according to the extended Hartree-Fock method in the -electronic approximation with consideration of electron correlation. The calculations confirm the deviation from Hund's rule observed for these compounds. The possibility of the application of the method indicated to the construction of many-electron functions with the correct symmetry in the case of orbital degeneracy has been discussed.Translated from Teoreticheskava i Éksperimental'naya Khimiya, Vol. 24, No. 2, pp. 208–211, March–April, 1988.     

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.     

Electronic structure and transport properties of early transition metal tripledeckers

The electronic structure and transport properties of the Cp(2)BzM(2) (M = Sc, Ti, and V) tripledeckers are studied by spin polarized density functional theory and nonequilibrium Green's function method considering high-spin and low-spin states. Total energy calculations show that the sandwich structured Cp(2)BzSc(2) exists in a singlet state with no local magnetic moment on the Sc atoms. Cp(2)BzTi(2) in triplet state exists as a distorted tripledecker and is more stable than singlet and quintet states. Cp(2)BzV(2) stabilizes in the quintet state with a spin density of 2.4 on each vanadium atom. Hund's coupling plays a vital role in stabilizing the higher multiplets in case of titanium and vanadium clusters. In bigger clusters like Cp(3)Bz(2)M(4), Sc multidecker has one unpaired spin, Ti multidecker has five unpaired spins, and V multidecker has seven unpaired spins in total. Spin polarized electronic transport is found for all states of vanadium tripledecker and one state of the titanium tripledecker when connected to a gold two probe junction. Moderate to high-spin filter efficiencies are calculated for these states. Cp(2)BzSc(2) shows spin-independent electronic transport for all electronic states when introduced in the gold two probe junction. Current versus voltage curves are reported for selected clusters in the two probe setup.     

Does chlorine peroxide absorb below 250 nm?

Low-lying singlet and triplet electronic excited states of ClOOCl are presented. Calculations of the excitation energies and oscillator strengths are reported using excited state coupled cluster response methods, as well as the complete active space self-consistent field method with the full Breit-Pauli spin-orbit operator. These calculations predict that for ClOOCl there should be a weakly absorbing triplet state lying below the lowest absorbing singlet excited state. This state is predicted to have an absorption maximum at about 385 +/- 25 nm. This lowest triplet state is calculated to be dissociative and leads to ClOO+Cl.     

Spectroscopic and electronic structure studies of the diamagnetic side-on CuII-superoxo complex Cu(O2)[HB(3-R-5-iPrpz)3]: antiferromagnetic coupling versus covalent delocalization

Magnetic, vibrational, and optical techniques are combined with density functional calculations to elucidate the electronic structure of the diamagnetic mononuclear side-on CuII-superoxo complex. The electronic nature of its lowest singlet/triplet states and the ground-state diamagnetism are explored. The triplet state is found to involve the interaction between the Cu xy and the superoxide pi v * orbitals, which are orthogonal to each other. The singlet ground state involves the interaction between the Cu xy and the in-plane superoxide pi v * orbitals, which have a large overlap and thus strong bonding. The ground-state singlet/triplet states are therefore fundamentally different in orbital origin and not appropriately described by an exchange model. The ground-state singlet is highly delocalized with no spin polarization.     

Spectroscopy and photophysics of dimethyl-substituted alloxazines

We have calculated the electronic structure and absorption spectra from the ground state and the first triplet excited state for five dimethylalloxazines, using the TD-DFT approach. The results of the calculations were correlated to experimental spectral and photophysical data, including the transient spectra reported here containing triplet–triplet absorption data, using the proximity effect theory to explain the variations of the ISC rates with the substitution pattern and solvent. Additionally, singlet oxygen yields were measured for these compounds, demonstrating their high efficiency as singlet oxygen photosensitizers.     

Convergence of third order correlation energy in atoms and molecules

We have investigated the convergence of third order correlation energy within the hierarchies of correlation consistent basis sets for helium, neon, and water, and for three stationary points of hydrogen peroxide. This analysis confirms that singlet pair energies converge much slower than triplet pair energies. In addition, singlet pair energies with (aug)-cc-pVDZ and (aug)-cc-pVTZ basis sets do not follow a converging trend and energies with three basis sets larger than aug-cc-pVTZ are generally required for reliable extrapolations of third order correlation energies, making so the explicitly correlated R12 calculations preferable.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Ab initio multireference investigation of disjoint diradicals: singlet versus triplet ground states

We present improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO‐CASCI) and IVO‐CASCI‐based multireference Møller–Plesset perturbation theory (MRMPPT) calculations with an aim to elucidate the electronic structure of tetramethyleneethane (TME) in its lowest singlet and triplet state and to quantify their order and extent of splitting. The potential surfaces of singlet and triplet states for the twisting of TME are also studied. We found that the triplet state is higher in energy than the singlet one in the whole range of twisting angles with the energy gap minimum at a twisting angle of about 45°. Harmonic vibrational frequencies of TME have also been calculated for both the states. We also report the ground to first excited triplet state transition energies. Our results are analyzed with respect to the results available in the literature to illustrate the efficacy of our methods employed. We also demonstrate that the spin character of the ground state of disjoint, TME‐like diradicals can be manipulated by using appropriate selection of annulenic spacer to separate the allyl groups of TME.     

The triplet state of cytosine and its derivatives: electron impact and quantum chemical study

The excitation of the lowest electronic states and vibrational excitation of cytosine (C) have been studied using electron energy loss spectroscopy (EELS, 0-100 eV) with angular analysis. The singlet states have been found to be in good agreement with UV-VIS absorption results on sublimed films, slightly blueshifted by about 0.1 eV. The EEL spectra recorded at residual energy below 2 eV show clear shoulders at energy losses of 3.50 and 4.25 eV (+/-0.1 eV). They are assigned to the lowest triplet electronic states of cytosine. Energies and molecular structures of the lowest-lying triplet state of C and its methylated and halogenated 5-X-C, 6-X-C, and 5-X, 6-X-C substituted derivatives (X=CH3, F, Cl, and Br) have been studied using quantum chemical calculations with both molecular orbital and density functional methods, in conjunction with the 6-311++G(d,p), 6-311++G(3df,2p), and aug-cc-pVTZ basis sets. The triplet-singlet energy gap obtained using coupled-cluster theory [CCSD(T)] and density functional theory (DFT) methods agrees well with those derived from EELS study. The first C's vertical triplet state is located at 3.6 eV, in good agreement with experiment. The weak band observed at 4.25 eV is tentatively assigned to the second C's vertical triplet excitation. For the substituted cytosines considered, the vertical triplet state is consistently centered at 3.0-3.2 eV above the corresponding singlet ground state but about 1.0 eV below the first excited singlet state. Geometrical relaxation involving out-of-plane distortions of hydrogen atoms leads to a stabilization of 0.6-1.0 eV in favor of the equilibrium triplet. The lowest-lying adiabatic triplet states are located at 2.3-3.0 eV. Halogen substitution at both C(5) and C(6) positions tends to reduce the triplet-singlet separations whereas methylation tends to enlarge it. The vibrational modes of triplet cytosine and the ionization energies of substituted derivatives were also evaluated.     

The Antiferromagnetic Spin Coupling in Non‐Kekulé Acenes—Impressive Polyradical Character Revealed by High‐Level Multireference Methods

Complete active space (CASSCF) and multireference (MR‐CISD(Q) and MR‐AQCC) calculations were performed for non‐Kekulé analogues of acenes, dimethylenepolycyclobutadienes, with lengths of up to eight cyclobutadiene (CBD) units. Multireference calculations predict that the most stable energy state of the system is either triplet (if there is an odd number of CBD units) or singlet (if there is an even number of CBD units) due to antiferromagnetic spin coupling, which thus violates Hund's rule in larger molecules. We also show an impressive polyradical character in the system that increases with the size of the molecule, as witnessed by more than eleven unpaired electrons in the singlet state of the molecule with eight CBD units. Together with the small energy gap between singlet and higher multiplicity energy states even above the triplet state, this demonstrates the exceptional polyradical properties of these π‐conjugated oligomeric chains.     

Singlet and triplet potential energy surfaces of C3H2

The detailed singlet and triplet potential energy surfaces of C₃H₂ involving nine isomers and 13 transition structures are studied at the G3 level of theory. The rearrangement mechanisms and the electronic properties of various isomers in a broad energy range have been studied in both singlet and triplet states. Cyclopropenylidene and propargylene are found to be the most stable isomers in the singlet and triplet states, respectively. The singlet isomers are found to be more kinetically stable species as a result of high conversion barriers through which they pass. The calculations indicate that cyclopropyne in its triplet state is the least kinetically stable isomer. It is realized that the G3 method comprises both computational cost and accuracy and thus can be applied to investigation of potential energy surface of small molecules.