The absorption and circular dichroism bandshapes of chromophore aggregates as studied by a modified Green's function theory

A modified Green's function method is applied to calculating the aggregate bandshape whereby a decoupling approximation for vibrationally averaging the Green's function is used to include thermal and static effects as well in terms of the correction shift of the chromophore bandshape. The utility of the present method is shown by a sample calculation of the absorption and circular dichroism bandshapes of a model dimer.     

Generalization of the bandshape expansion formula for the circular dichroism of chromophore aggregates

A generalized expression of the bandshape expansion formula for the circular dichroism of chromophore aggregates is derived using an extended Green's function method. Basic properties of the generalized bandshape expansion formula are studied in comparison with the perturbation expansion equation given by the usual decorrelation approximation.     

Isometric groups and chirality of nonrigid molecules: a generalization of Kelvin's theorem

A generalization of Kelvin's theorem for the chirality of rigid molecules to nonrigid molecules is given. It is based on the concept of the isometric group of nonrigid systems which allows a formulation of the chirality criterion of nonrigid systems in close analogy with Kelvin's original formulation. A number of examples, in particular such as investigated by Mislow, are given.     

Series expansion calculation of the elastic neutron diffuse scattering: Ice Ih

A theoretical systematic method for the evaluation of the neutron elastic, coherent, diffuse scattering intensity of ice Ih is presented. For each Q vector, the latter is expressed directly as a series expansion of graphs. This technique is analogous to the Ising susceptibility calculation and avoids the explicit use of individual correlation functions. Therefore the series can be easily and exactly expanded to rather high orders. For the computation of the scattering intensity, the correlation model used is based on the ice rules and the normalized probability is written according to Nagle's formulation. The resulting series is convergent and theoretical isodiffusion patterns have been drawn by extending the series up to the 8th order; the accordance with experiment is good.     

Topological effects displayed in absorption and photoelectron spectra

For topologically related pairs of isomers, S and T, a theorem we term TEMO (Topological Effects on Molecular Orbitals) has been derived; it organizes the MO pattern of the isomers so that in the range of two subsequent MO's of S there are alternately two and no MO's of T. It follows that depending on the number of electrons, the HOMO-LUMO separation in S and T differs in a topologically determined manner. The wave-lengths of the absorption maxima of the longest wave-length transitions in polycyclic aromatic hydrocarbons, polymethines, and heterocyclic compounds are in accord with TEMO. The photoelectron spectra of these compounds exhibit the TEMO pattern of their MO's even in cases where Koopmans' theorem fails.     

Inversion-free formulation of the direct recursion (transfer matrix) method

The transfer matrix or direct recursion methods (DRM), the indirect (exact) perturbation methods (IPM) and the indirect recursion methods (IRM) — the latter two commonly called resolvent or Green function methods — are briefly discussed. Lee and Joannopoulos have shown the very computational advantages of a traditional DRM. For its further improvement, a new inversion-free DRM (IF DRM) is proposed which is based on the application of generalized eigenvalue equations. In the present formulation, the IF DRM is applicable to study surface electronic problems of bounded perfect crystals. The method of the framework translation is also described which avoids the Schmidt—Hori—Asahi-type transfer matrix trick. It is convenient to study layered structures. Finally, the advantages of a new IRM are stressed which also avoids the inversion difficulty.     

Circular dichroism spectra of DNA hairpins studied by the green function method

The circular dichroism (CD) spectrum of a large biological molecule represented as an array of interacting chromophores is investigated. The configuration-averaged Green function formalism is developed to describe the CD and absorption spectra. The perturbation theory expansion is derived for absorption and CD spectra in the case of strong interaction of chromophores with their environment (solvent and/or internal dynamics) compared to their interaction with each other. We apply this formalism to study CD spectra of DNA hairpins.     

A combined SAMO-ZDO method for the evaluation of ionization potentials

A scheme for the ab initio calculation of vertical ionization potentials without the necessity to compute two-electron repulsion integrals is discussed. The method employs the simulated ab initio molecular orbital (SAMO) method to generate Koopman's theorem eigenvalues. These are then corrected for the change in relaxation and correlation effects due to ionization by a Green's function perturbation scheme, in which all necessary integrals are evaluated using the zero differential overlap (ZDO) approximations, in this case the complete neglect of differential overlap (CNDO) method.     

Vibrational relaxation of hydrogen-bonded species in solution. I. Theory

We present a simple model to describe the phase relaxation of the ν_s(XH) mode of a hydrogen-bonded species XH?Y in solution in an inert solvent. The major assumptions made are that the ν_σ(XH?Y) stretching mode of the hydrogen bond can be represented by the Ornstein—Uhlenbeck stochastic process, and that the ν_s(XH) phase coherence is lost because of the coupling between the two vibrational modes. The model can be analysed in terms of Kubo's theory of a randomly modulated oscillator. An expression is derived for the transition dipole moment autocorrelation function which characterises the line shape of the mid infrared ν_s(XH) absorption band, and various limiting cases of the formula are discussed. It is further shown that vibrational relaxation may be expected to influence the far infrared ν_σ(XH?Y) bandshape and the one-phonon neutron inelastic scattering cross section, and that the parameters required to characterise all three types of spectra are closely related. Experimental tests of the theory are reported in the following paper.     

Calculation of the HeI photoelectron spectrum of CS including satellite lines

The ionization potentials and the vibrational structure in the photoelectron spectrum of the CS molecule aer calculated using a Green's function approach. The inclusion of many-body corrections to Koopmans' theorem is necessary in order to obtain the correct ordering of the first two ionization potentials. In contrast to previous interpretations of the spectrum the third band has to be assigned to a shake-up line and the fourth to the 6σ orbital. The calculated vibrational structure is in good agreement with experiment and corroborates this assignment.     

Multiple substitution effects in configuration interaction calculations

The common way of approximating multiple substitution effects by the unlinked cluster contribution based on the linked cluster theorem is investigated. Formally the analysis is done in a configuration interaction language without reference to diagrams. Using the linked cluster theorem a series expansion is then developed for the correction of a CI calculation, including double replacements only, for the erratic treatment of unlinked clusters. The first term in this series is closely related to what is generally referred to as Davidson's correction. The next term is proportional to the square of the correlation energy and is also very easy to calculate. Finally numerical examples are given illustrating the accuracy of the different approximations.     

A Pascal type triangle for the number of topologically distinct many-electron Feynman graphs

By expressing the Green function for a many-body system in terms of a perturbative expansion written as a sutra over all connected and topologically distinct Feynnian graphs, it is shown that the number of such diagrams can be iteratively obtained from a Pascal-type triangle, The key to the problem is to notice that it is possible to define on the set of graphs an equivalence relation, and that, from a well-known theorem of set theory, an equivalence relation on a set partitions it into disjoint classes.     

Estimation of the Moments of the Residence Time and First Passage Time from Experimentally Measurable Permeation Parameters via a New Formulation of the Transmission Matrix

Siegel's analysis on membrane transport in the Laplace domain [J. Phys. Chem. 95 (1991) 2556] in terms of transmission matrix, T(s), has been extended to a more useful formulation. This is achieved by combining uses of the matrix transport equations appropriate for void initial condition, or for saturated equilibrium, or of Dirac delta functional type and the theorem det[T(s)] = 1. This formulation enables us to expand T(s) in power series of the Laplace variable, s, with the expansion coefficients as the algebraic functions of the experimentally measurable transport parameters. Utility of the formulation is illustrated in the estimation of the experimentally inaccessible time moments for the first passage or residence times. It was also applied to the percutaneous drug delivery to obtain from the experimental data. The higher moments of the time lag or time lead using a graphic method.     

Symmetry adapted formulation of the generalized Brillouin theorem

The singly excited functions satisfying Brillouin theorem are expressed as linear combinations of configuration-state functions for any spin and spatial symmetries (atomic or molecular) and for any reference wave function. The generality of the formulation is ensured by the use of the irreducible tensor method that can be adapted to any symmetry point group of interest. The expansion coefficients are simply written as products of fractional parentage coefficients, spin- and orbit-recoupling coefficients, and phase factors. The formalism is illustrated for some atomic (K_h) and molecular (C_∞v, C_3v, and T_d) configurations. Group theoretical techniques are also used to correlate the Brillouin conditions within a chain of groups.     

A naive look on the Hohenberg–Kohn theorem

A generalised Hohenberg–Kohn theorem is described in terms of the sign of the secondorder energy variation. Independently, it is also corroborated within the perturbation theoretical framework. An alternative formulation of the Hohenberg–Kohn theorem, based on the relationships involving the matrix representations of density functions and the Hamiltonian operator variations, is shown to extend the validity of the theorem to the excited states of the Hamiltonian operators possessing nondegenerate spectra. Finally, a connection with Brillouin's theorem when energy variation becomes stationary is also outlined.     

A proof of pitzer's theorem for abelian groups and its application to two-electron integral transformation

Pitzer's theorem is proved for abelian groups. The expression obtained can be used to perform the two-electron integral transformation taking advantage of molecular symmetry by a single-step procedure.     

A note on the temperature dependence of the coordination number

An empirical equation describing the temperature dependence of the coordination number of a molecule in a liquid is examined in terms of Bernal's model for the liquid state. To effect this comparison the non-associated compound n-C₁₁H₂₄ is chosen to represent the temperature span of the empirical equation. Predictions from Bernal's model based on volume expansion and latent heat data are in good agreement with the empirical correlation.     

Local and average electromagnetic enhancement in surface-enhanced Raman scattering from self-affine fractal metal substrates with nanoscale irregularities

We study the electromagnetic mechanism in surface-enhanced Raman scattering (SERS) from random self-affine fractal metal substrates with nanoscale irregularities by means of the rigorous Green’s theorem integral equation formulation. The SERS enhancement factor is calculated from the numerical results for the surface electric field intensity at the pump frequency for ensembles of self-affine fractal realizations a few microns wide with decreasing lower scale cutoff. We observe a dramatic increase of the local and average SERS enhancement factors throughout the visible and near infrared when the size of surface irregularities is diminished to a few nanometers.     

Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S‐matrix and the associated Green function. The performance of the Mittag–Leffler expansion and T‐matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s‐wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag–Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S‐matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007