M. Bixon

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...

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.

Long Radiative Lifetimes of Small Molecules

In this paper, we apply a theory of electronic relaxation in polyatomic molecules for the study of the anomalously long radiative lifetimes of NO2, CS2, and SO2. We have classified medium‐size molecules which exhibit intramolecular vibronic coupling into two intermediate cases, which we call the sparse intermediate case and the dense intermediate case, characterized by low and high spacing of the vibronic levels relative to the radiative width. The radiative decay in the sparse intermediate case was considered in detail, taking advantage of the coarse level spacing and the extremely short intramolecular recurrence time encountered in this case. From our model calculations, we conclude that:(a) in the sparse case, the radiative decay rate is characterized by a superposition of slowly varying exponentials;(b) the mean radiative lifetime is expressed as a radiative lifetime calculated from the integrated oscillator strength and “diluted” by the number of states within the half‐width of the manifold of couple...

Potential functions and conformations in cycloalkanes

Abstract Energy functions of bending of the C—C—C angle and of twisting of the CH2—CH2 torsional angle have been examined through their effect on calculations of stable conformations and excess enthalpies of all the cycloalkane molecules from C6H12 to C12H24. The total strain energy was expressed as a function of the internal coordinates—bond lengths, bond angles and torsional angles. H—H distances were derived by matrix algebra, and the method of steepest descent was applied. Energy parameters like the bending force constant, the zero-strain value of bond angles, torsional potential barrier, were varied one at a time, and their effect on conformation and strain energy examined. Results have been compared with calorimetric measurements and with Xray and electron diffractions. Enthalpy of translation-rotation-vibration was also considered and found to be significant. Best agreement between calculations and experiment was obtained when the energy parameters were derived from n-alkanes. Thus, the n-alkane bond angle value of 112·7° is preferable to the tetrahedral angle as the zero-strain value; the torsional potential barrier of propane, 3·4 kcal/mole, is preferable to the corresponding value for ethane, 2·8 kcal/mole.

Unidirectionality of charge separation in reaction centers of photosynthetic bacteria

Abstract Time-resolved spectroscopy in conjunction with X-ray structural data for reaction centers of Rhodopseudomonas viridis and Rhodobacter sphaeroides reveal a branching ratio a > 5 for the primary electron-transfer rates, favouring one of the two, almost symmetrical pigment/protein branches, L and M. In this paper we explore the origins of this unidirectionality of electron transfer between the excited singlet state of the bacteriochlorophyll dimer ( 1 P∗) and the bacteriopheophytin (H) along the L protein subunit. Nonadiabatic electron-transfer theory is applied to analyze the asymmetry of the electron-transfer rates, k L and k M across the L and M branches. The asymmetry originates from the cumulative contributions of the nuclear Franck-Condon factor and the electronic coupling, both of which enhance the electron transfer rate across the L branch. The nuclear Frank-Condon factors are modified by the energy difference ΔE LM between the states P + H − L and P + H − M , which is induced by the electrostatic interactions of these ion-pair states with the protein polar groups, as well as by asymmetric Coulomb and medium polarization interactions. The computation results in ΔE LM = −(0.09 ± 0.04) eV, which yields a nuclear enhancement contribution at 300 K of 1.5 (+0.8, −0.3) to k L k M and therefore is insufficient to explain alone the observed asymmetry in reaction centers of Rps. viridis . Another contribution to the unidirectionality originates from electronic superexchange coupling for 1 P∗-B-H via the virtual states of the accessory bacteriochlorophyll (B). The ratio of the intermolecular 1 P∗-B L and 1 P∗-B M electronic interaction terms was evaluated utilizing the tight-binding approximation with SCF-MO wavefunctions, together with the structural data for the prosthetic groups and for the polar amino acid side chains of the protein in reaction centers of Rps. viridis . The contribution to the enhancement of k L k M by the electronic superexchange is approx. 8 ± 4. This asymmetry was traced to the combination of an excess negative charge density on the M-dimer component P M , together with structural asymmetry, which enhances the P M -B L electronic overlap. Consequently, the 1 P∗-B L -H L superexchange is favoured over the 1 P∗-B M -H M interaction. The combined effects of asymmetric nuclear Franck-Condon factors and electronic couplings yield a branching ratio of the electron-transfer rates along the two pigment branches in reaction centers of Rps. viridis of an approx. 12 (−7, +15). This is sufficiently large to explain the experimentally observed unidirectionality.

On the mechanism of the primary charge separation in bacterial photosynthesis

In the light of recent experimental work on femtosecond electron transfer kinetics in the reaction center (RC) we explore the mechanism for the primary process. We focus on the special role of the bacteriochlorophyll monomer (B) located between the primary donor ( 1 P*), a bacteriochlorophyll dimer (P), and a bacteriopheophytin (H), considering a kinetic scheme which combines two parallel pathways of electron transfer: a unistep superexchange channel mediated via electronic interactions with P + B − H, and a two-step sequential channel involving a P + B − H chemical intermediate. In this kinetic scheme we used microscopic nonadiabatic electron transfer rates, which were extended to incorporate the effects of medium-controlled dynamics. The results of the kinetic modelling are presented as a function of the free-energy gap Δ G 1 between the equilibrium nuclear configurations of the donor 1 P* BH and the (physically and/or chemically) mediating state P + B − H. The parallel sequential-superexchange mechanism reduces to the limit of nearly pure sequential pathway for large negative Δ G 1 at all temperatures and to the limit of almost pure superexchange pathway for large positive Δ G 1 at all temperatures and for moderate Δ G 1 at low temperatures. The existing femtosecond kinetic data at room temperature are consistent with either the superposition of sequential and superexchange at all temperatures or to a superposition of superexchange and sequential at room temperature and superexchange at low temperatures. The available femtosecond data at 10 K raise the possibility that the mechanism involves the superposition of superexchange and sequential at 300 K and the dominance of superexchange at low temperatures. Auxiliary experimental information regarding magnetic data, i.e., the singlet-triplet splitting of the radical pair P + BH − , the kinetics of the charge separation in mutagenetically altered RCs, with tyrosine M208 being replaced by phenylalanine, and the unidirectionality of charge separation across the A branch of the RC are analysed in terms of the proposed mechanism. The prevalence of the parallel sequential and superexchange electron transfer routes for the primary charge separation would introduce an element of redundancy, which insures the occurrence of an efficient process which is stable with respect to the variation energetic parameters in different photosynthetic RCs.

Electronic coupling between Watson–Crick pairs for hole transfer and transport in desoxyribonucleic acid

Electronic matrix elements for hole transfer between Watson–Crick pairs in desoxyribonucleic acid (DNA) of regular structure, calculated at the Hartree–Fock level, are compared with the corresponding intrastrand and interstrand matrix elements estimated for models comprised of just two nucleobases. The hole transfer matrix element of the GAG trimer duplex is calculated to be larger than that of the GTG duplex. “Through-space” interaction between two guanines in the trimer duplexes is comparable with the coupling through an intervening Watson–Crick pair. The gross features of bridge specificity and directional asymmetry of the electronic matrix elements for hole transfer between purine nucleobases in superstructures of dimer and trimer duplexes have been discussed on the basis of the quantum chemical calculations. These results have also been analyzed with a semiempirical superexchange model for the electronic coupling in DNA duplexes of donor (nuclobases)–acceptor, which incorporates adjacent base–base el...

Electronic Relaxation in Large Molecules

In this paper we consider the problem of the radiative decay of electronically excited states of a large molecule. We have considered both intramolecular vibronic coupling and the interaction with the radiation field. Compound states for a system of decaying indistinguishable levels are constructed using the Fano method. General expressions for the radiative decay rate are derived and applied for the statistical limit of intramolecular vibronic coupling. On a time scale shorter than a typical intramolecular recurrence time the radiative decay is exponential, and the reciprocal lifetime consists of independent contributions of radiative and nonradiative components. The experimental implications of these results for large and medium‐size molecules are discussed.

Energetic and thermodynamic size effects in molecular clusters

In this paper we explore the interrelationship between the energetics and the thermodynamic properties of molecular clusters. We advance simple models for the energy spectrum, which are used to derive analytical results for the thermodynamic properties of these clusters. The energy spectrum is characterized by the distribution of the energies of the local minima of the nuclear potential energy hypersurface, i.e., the inherent structures. On each of these energy levels the vibrational density of states of the particular inherent structure is superimposed. The energy spectra were specified in terms of the energy gap, Δ, between the (single) ground state and the excited‐state inherent structures, the number, R, of the inherent structures and their energetic spread W. Four classes of energy spectra were considered. (1) A large energy gap with nearly degenerate excited‐state manifold, i.e., Δ≫W. (2) A large energy gap with a considerable spread of the excited‐state manifold, i.e., Δ≪W and W/R≪Δ. (3) A gapless ...

Optimized Rouse–Zimm theory for stiff polymers

Earlier, the authors proposed a method for constructing an optimized Rouse–Zimm theory for an arbitrary polymer system. This method is applied here to a model of a stiff polymer. The spectrum of relaxation times and the intrinsic viscosity obtained from the optimized Rouse–Zimm theory are discussed. Comparison with known results for the limiting cases of a flexible chain, a rigid ring, and a rigid rod, shows that this procedure gives a quite good approximation at low frequencies. Its basic disadvantage is its inability to account for the observed high frequency behavior of the intrinsic viscosity of stiff polymers.