Joshua Jortner

The energy gap law for radiationless transitions in large molecules

In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangeme...

Intramolecular Radiationless Transitions

In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero‐order excited states are not pure in view of configuration interaction between nearly degenerate zero‐order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero‐order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the inte...

Temperature dependent activation energy for electron transfer between biological molecules

This paper considers electron transfer between biological molecules in terms of a nonadiabatic multiphonon nonradiative decay process in a dense medium. This theoretical approach is analogous to an extended quantum mechanical theory of outer sphere electron transfer processes, incorporating the effects of both low‐frequency medium phonon modes and the high‐frequency molecular modes. An explicit, compact and useful expression for the electron transfer probability is derived, which is valid throughout the entire temperature range, exhibiting a continuous transition from temperature independent tunneling between nuclear potential surfaces at low temperatures to an activated rate expression at high temperatures. This result drastically differs at low temperatures from the common, semiclassical, Gaussian approximation for the transition probability. The experimental data of De Vault and Chance [Biophys. J. 6, 825 (1966)] on the temperature dependence of the rate of electron transfer from cytochrome to the chlo...

The effect of intramolecular quantum modes on free energy relationships for electron transfer reactions

A general quantum mechanical description of exothermic electron transfer reactions is formulated by treating such reactions as the nonradiative decay of a ’’supermolecule’’ consisting of the electron donor, the electron acceptor, and the polar solvent. In particular, the role of the high‐frequency intramolecular degrees of feedom on the free energy relationship for series of closely related reactions was investigated for various model systems involving displacement of potential energy surfaces, frequency shift, and anharmonicity effects. The free energy plots are generally found to pass through a maximum and to be asymmetric with a slower decrease in the transition probability with increasing energy of reaction. For high‐frequency intramolecular modes this provides a rationalization of the experimental observation of ’’activationless’’ regions. Isotope effects are discussed as also are the oscillatory free energy relationships, predicted for low temperatures and high frequencies, and which are analogous t...

Dynamic solvent effects on outer‐sphere electron transfer

In this paper we present the results of a theoretical study of outer‐sphere electron transfer (ET) in a polar solvent, with the modification of the nuclear states by the change in the charge distribution originating solely from the response of the exterior medium. The model Hamiltonian for the system corresponds to two parabolic diabatic potential surfaces with adiabatic coupling between them. The real‐time path integral formalism is utilized to derive the general expressions for the influence functional of the medium in the Gaussian approximation and for the ET rate. The ET rate is explicitly evaluated for the particular case of a medium characterized by the Debye dielectric relaxation function. We explore the relation between the dynamics of the reaction coordinate and the character of the ET process, deriving an expression for the ET rate, which bridges between the nonadiabatic and the solvent‐controlled adiabatic limits. We establish simple criteria for the validity range of various descriptions of ET...

Multiphonon Processes in the Nonradiative Decay of Large Molecules

Radiationless transition rates for polyatomic molecules are investigated in the simplest case of the statistical limit, i.e., large energy gaps between the two electronic states. By analogy with the theory of optical line shapes in solids, the “golden rule” rate expression for the nonradiative decay, which is usually written as a double sum over initial and final vibronic states, is equivalently represented in closed form as a single Fourier integral. For the case in which the vibrations are assumed to be harmonic, but may have different frequencies and equilibrium positions in the two electronic states, general closed‐form analytic expressions, which include all of the vibrational modes, are obtained for the transition rates. The energy gap law is again obtained in the weak coupling statistical limit along with a proper description of the propensity rules for the promoting mode. For the case of the aromatic hydrobarbons, the effective energy gap is found to be in agreement with Siebrands analysis, and e...

Cooling of large molecules below 1 K and He clusters formation

We present here the design details of a high-pressure pulsed valve that generates intense supersonic jets. The measured rotational contours of Aniline indicate that temperatures lower than 0.5 K can be achieved before the formation of clusters with the He carrier gas. The spectral shifts and vibronic structure of Anthracene–Hen clusters (n=1–6) are showing some surprising features.

Intramolecular vibrational excitations accompanying solvent‐controlled electron transfer reactions

The theory of dynamic solvent effects on outer‐sphere electron transfer (ET) was extended to incorporate the modification of the high‐frequency quantum modes, which is manifested by the reduction of the electronic coupling by nuclear Franck–Condon factors and by the change of the energy gap. Explicit expressions for the ET rates were obtained in terms of a sum over parallel vibronic channels, each involving a distinct intramolecular vibrational excitation of the final state. In the solvent‐controlled adiabatic limit, the effects of intramolecular vibrational excitation are exhibited by the modification of the (partial) activation energies, while the frequency factor is dominated by the longitudinal dielectric relaxation rate of the solvent.

Cluster size effects

In this paper we address some of the unique, novel and basic features of clusters, which involve the physical and chemical consequences of their large surface/volume ratio and the size dependence of the properties of large finite systems. Energetic, quantum, electronic, spectroscopic, and electrodynamic size effects in clusters were quantified by cluster size equations (CSEs), which describe the gradual “transition” from the large finite cluster to the infinite bulk system, with increasing the cluster size. Some progress was also accomplished in the description of the “transition” from cluster microsurfaces to macrosurfaces, which can be described in terms of surface CSEs. The analysis implies a nonuniversality principle for cluster size effects, with different physical properties being described in terms of distinct CSEs. The CSEs provide a quantitative answer to a central question in the area of cluster chemical physics: What is the minimal cluster size for which its properties become size invariant and do not differ in any significant way from those of the macroscopic sample of the same material? A unified (but not universal) description is advanced for the merging between the properties of microscopic large finite systems and those of a macroscopic bulk material.

Triplet Excitons in Crystals of Aromatic Molecules

In the present paper we consider the band structure and the Davydov splitting of the first triplet exciton states in crystalline naphthalene, anthracene, and biphenyl. It is found that: (a) An important contribution to the triplet exciton bandwidth arises from intermolecular exchange interaction. These interactions are calculated in the molecular orbital π‐electron approximation. (b) Excitation exchange effects due to spin—orbit coupling are negligible. (c) Nonorthogonality corrections, considered within the framework of the symmetric orthogonalization procedure, have been found to be small. (d) Crystal‐field mixing of triplet states arising from π→π* excitations has no effect on the triplet bands. (e) An important contribution to the triplet exciton bandwidth may arise from configuration interaction with charge‐transfer states.The dynamics of triplet excitons in aromatic crystals was studied in the two limiting cases of strong and weak scattering. The band model, with the constant mean‐free‐path approxim...