Shmuel Zilberg

Twin states and conical intersections in linear polyenes

Abstract We suggest for linear conjugated polyenes a twin state model which represents the ground state (S 0 ) and first excited state (S 1 ) as a superposition of mainly two mesomeric structures, the fully spin-paired one and a diradical. This model rationalizes why the bond-length alternation, which is pronounced in S 0 , more or less disappears in S 1 and why the bond-alternation vibration (highest frequency CC stretch) is raised in S 1 and depressed in S 0 . The similarity to the Peierls effect and Kohn anomaly in one-dimensional metals is emphasized. Moreover, the conical intersection between S 2 and S 1 is qualitatively predicted, and invoking in addition, some spectroscopic and other observations and the phase-change rule, that between S 1 and S 0 can also be predicted. Compared with the consideration of densities of states and matrix elements, these intersections more satisfactorily explain the S 2 /S 1 and S 1 /S 0 internal conversions and their dependence on chain length, substituents, solvent and temperature and is furthermore consistent with photochemistry. This also includes an exponential gap rule for the internal-conversion rates, which is derived from a proposed dependence of the energy at the intersection on the S 1 –S 0 energy gap.

Ab initio study of styrene and β‐methyl styrene in the ground and in the two lowest excited singlet states

The structure and vibrational frequencies of styrene and trans‐β‐methyl styrene in the lowest three singlet states (S0, S1, and S2) have been calculated using ab initio quantum chemical methods. The frequencies are compared with experimental data obtained in the bulk and in a supersonic jet. The calculation shows that in the ground state the molecules have a broad shallow potential as a function of the torsional angle, are essentially planar, but may be slightly bent. In the S1 and S2 states, the molecules are planar; In S1, the main structural change is in the aromatic ring, that is somewhat expanded. In S2, the C=C vinyl double bond elongates, while the C1—Cα single bond becomes shorter, bringing these two bonds to almost equal length. Correlation diagrams connecting ground state vibrational modes with ones belonging to electronically excited states are given; they show that for many out‐of‐plane modes the vibrational frequencies decrease upon electronic excitation. This is accounted for in terms of the...

Stability of Polynitrogen Compounds: The Importance of Separating the σ and π Electron Systems

Planar N(x) systems such as cyclo-N(5)(-) and N(5)(+) tend to be more stable than nonplanar systems such as the neutral cyclo-N(6). It is proposed that the key to stabilization is the separation of the sigma and pi electron systems. In both cyclo-N(5)(-) and N(5)(+), a six-pi-electron system is created upon either adding to or removing from the cyclo-N(5) radical one electron. Judicious addition of oxygen atoms to polynitrogen ring compounds such as cyclo-N(4) and cyclo-N(6) can increase their thermodynamic and kinetic stabilities, accompanied by only a small reduction in their efficiency as high energy density materials (HEDMs). The properties of some of these compounds are calculated and compared with the parent all-nitrogen compounds. Coordination of one or more oxygen atoms to the ring leads to effective separation of the sigma and pi electron systems helping to stabilize the systems. Natural bond analysis indicates that the exocyclic NO bonds can assume a single or double bond character, depending on the ring system.

Molecular Photochemistry: A General Method for Localizing Conical Intersections Using the Phase-Change Rule

Conical intersections are of central importance in many photochemical processes. A simple means for localizing them is offered; it is based on the phase-change rule of Longuet-Higgins. Triple- and single-phase-change loops can be constructed and can be applied to various different systems. A single-phase-change loop is shown schematically in the figure.

Photoreactivity of a Push-Pull Merocyanine in Static Electric Fields: A Three-State Model of Isomerization Reactions Involving Conical Intersections

The photochemistry of a prototype push-pull merocyanine is discussed using a simple three-state model. As a derivative of butadiene, the model focuses on two isomerization reactions around the two double bonds of the butadiene backbone. As a molecule substituted by an electron donor and electron acceptor at opposite ends, its structure as well as its photochemistry are expected to be strongly affected by the environment. In polar solvents, a zwitterion transition state for each of the isomerization reactions is stabilized, and its energy is on the same order as that of the biradical one; this leads to the symmetry allowed crossing (S(0)/S(1) conical intersection). It is shown that applying an external electric field or varying the solvent polarity changes the relative energies of the different transition states as well as that of the conical intersection, and thus different photochemical products can be obtained. In particular, the very existence of conical intersections is found to depend on these external parameters. This work provides a theoretical foundation for ideas expressed by Squillacote et al. (J. Am. Chem. Soc. 2004, 126, 1940) concerning the electrostatic control of photochemical reactions.

The Twin‐Excited State as a Probe for the Transition State in Concerted Unimolecular Reactions: The Semibullvalene Rearrangement

A twin of the transition state, which can be investigated spectroscopically and can thus supply information about the structure of the transition state, has now been characterized for the Cope rearrangement of semibullvalene (shown below). It involves an excited state with B2 symmetry and results from a linear combination of the ground-state wave functions of (mirror-image) reactant and product.

The vibrational structure of the S0 → S1 transition of anthracene

Abstract An ab initio calculation of the energy, geometry and vibrational frequencies of anthracene in the ground and first excited singlet state is presented, and compared with recent matrix isolation fluorescence results. It is found that a single configuration can reproduce the experimental data for S1 reasonably well: the 0,0 transitions energy is within 3% of the experimental value, and most observed vibronic bands in S1 can be assigned. The calculation helps to clarify some peculiarities of previous assignments, particularly for modes of the b1g symmetry. Some bands observed in the supersonic jet and in the matrix, and showing anomalously long decay times and unusual matrix shifts are found to fit with the calculated b3g modes. It is tentatively suggested that they are due to Herzberg-Teller vibronic coupling with a B1u+ state, whose presence is indicated in a recent synchrotron fluorescence excitation study.

Electrophilic Aromatic Substitution: The Role of Electronically Excited States

Electrophilic aromatic substitutions (EAS), one of the most extensively studied organic reactions, can be considered under certain circumstances as a photochemical reaction without light. Thermochemical considerations show that in the gas phase, the reaction system (electrophile plus aromatic neutral) is often found initially in an electronically excited state, whereas the reaction products are formed on the ground state potential energy surface (PES). The crossing to the ground state is usually very rapid, so that the rate-determining steps take place on the ground state surface. It is shown that after the crossing (through a conical intersection (CI)), the system can be found on different parts of the ground state potential surface. In particular, the CI is connected without a barrier to all moieties assumed to be important in the reaction (pi complex, radical pair, and sigma complex). In some cases, due to a relatively low electron affinity of the electrophile and bond reorganization, the reaction starts on the ground state PES; a conical intersection exists in these cases, but is not accessed by the reactants. The topology of the reaction surface due to the avoided crossing is reminiscent of that in which an actual crossing takes place. The paper provides a comprehensive model for several EAS reactions. The CIs are located computationally, and an energy level diagram is proposed for some representative EAS reactions.

S0↔S1 transition of trans‐β‐methyl styrene: Vibronic structure and dynamics

The fluorescence excitation and emission spectra of trans‐β‐methyl styrene have been measured in a supersonic jet. A complete vibrational assignment of the S0 and S1 states’ frequencies is reported, assisted by ab initio quantum chemical calculations and by comparison with the IR spectrum. The fluorescence lifetime, τf, of the isolated molecule changes monotonously from 24.5 to 15 ns as the excitation energy increases from the origin band to an excess of 3000 cm−1. The fluorescence quantum yield from the zero‐point energy level of S1 is about 38%, similar to the liquid solution value; The major radiationless process being intersystem crossing to a triplet level. The increasing congestion of the emission spectra as the excitation energy is increased is interpreted as due to intramolecular vibrational energy redistribution. The data are consistent with the fact that in the isolated molecule intramolecular vibrational energy redistribution is faster than intersystem crossing. Beyond an excess energy of about...

Isomerization around a CN double bond and a CC double bond with a nitrogen atom attached: thermal and photochemical routes

The Longuet-Higgins phase change theorem is used to show that, in certain photochemical reactions, a single product is formed via a conical intersection. The cis-trans isomerization around the double bond in the formaldiminium cation and vinylamine are shown to be possible examples. This situation is expected to hold when the reactant can be converted to the product via two distinct elementary ground-state reactions that differ in their phase characteristics. In one, the total electronic wavefunction preserves its phase in the reaction; in the other, the phase is inverted. Under these conditions, a conical intersection necessarily connects the first electronic excited state to the ground state, leading to rapid photochemical isomerization following optical excitation. Detailed quantum chemical calculations support the proposed model. The possibility that a similar mechanism is operative in other systems, among them the rapid photo-induced cis-trans isomerization of longer protonated Schiff bases (the parent chromophores of rhodopsins), is discussed.