David A. Rabenold

Unified Treatment of van der Waals Forces between Two Molecules of Arbitrary Sizes and Electron Delocalizations

Publisher Summary This chapter presents a unified treatment for the interaction between two non-overlapping molecular systems of arbitrary sizes and electron delocalizations. The theory is formulated on the basis of a generalization of the reaction-field technique developed earlier and results are expressed in terms of spatially dependent susceptibilities. The present approach is an infinite-order perturbative method which, in the absence of resonance interaction, yields an expression for the interaction (free) energy in terms of the properties of the noninteracting system. A rigorous expression is derived for the second-order free energy at finite temperatures and an approximate closed-form expression is obtained for the perturbation series by invoking the decorrelation approximation which neglects correlations between virtual excitations within each molecule. Special forms are derived for the dipolar approximation and the results are found to agree with previously derived results obtained by other methods. The connection between the reaction-field approach and those formulations based on collective behavior is discussed.

Extension of the matrix theory of circular dichroism for unordered polypeptides

A Green operator technique used within a susceptibility framework is employed to present a unified theory for the circular dichroism of unordered polypeptides. The theory includes ground state wave function corrections. Two limiting cases of the formulation are the matrix theory of CD and a generalization of the rotational strength expressions derived by Tinoco [Adv. Chem. Phys. 4, 113 (1962)].

Helical polymer circular dichroism: Transition matrix theory for polypeptides

A Green operator technique used within a linear response framework is employed to present a transition matrix theory of long helical polymer circular dichroism. Specializing to a polypeptide, simple closed form expressions are obtained for the circular dichroism. The formulation clearly shows (1) how the ΠΠ* exciton system gives rise to the ’’helix band’’ and ’’radial bands’’; (2) how the coupling of the ΠΠ* and nΠ* transition densities gives rise to a band centered at the unperturbed nΠ* transition frequency which is balanced in rotational strength by bands at the ΠΠ* perpendicular and parallel polarized transition frequencies; and (3) how interaction of these low energy transitions with high energy transitions can alter all of the above mentioned bands.

Linear response theory of polypeptide circular dichroism: Bogoliubov exciton theory

A linear response theory of polypeptide circular dichroism is presented. The Bogoliubov collective excitation theory is derived without the use of second quantization techniques and therefore direct insight to the approximations is obtained. The static field at each chromophore is approximated as an external field unaffected by the polarization it induces. Susceptibilities that contain the static field effect are obtained via a Green operator method. These susceptibilities are then used in the geometric expansion of time dependent Hartree theory to obtain the result. Also, a partitioning technique is presented for handling the resulting normal mode problem.

Circular and elliptical dichroism of partially oriented helical polymers

A linear response theory for the circular and elliptical dichroism of partially oriented helical polymers is presented. Circular and elliptical dichroism arise for light propagating parallel and perpendicular, respectively, to the direction of orientation. Expressions are presented for the difference of the oriented and unoriented circular dichroism. Specializing to polypeptide systems we provide a firm theoretical foundation for resolution of oriented circular dichroism spectra into component bands.

Linear response theory of dye–polymer complex circular dichroism

A linear response theory for the circular dichroism of dye–polymer complexes is presented. The time dependent Hartree approximation is employed and the effect of electrostatic fields is included in an approximate manner. Periodic boundary conditions are used to describe the polymer which may have several chromophores per repeating unit and any number of bound dye molecules. A partitioning technique is used to obtain the two components of the circular dichroism, that of the dye aggregate which is shifted due to dye–polymer interaction. The induced circular dichroism predicted by a less accurate scheme, a matrix approach, is shown for a typical case to be at least 24% less intense than that predicted by the time dependent Hartree scheme.

Circular dichroism theory for unordered polypeptides: A Green operator technique

A Green operator technique used within a suspectibility framework is employed to express the circular dichroism of a diamide which is taken as a model for an unordered polypeptide system. The formulation contains all common mechanisms that give rise to circular dichroism and has the advantage that band shape functions can be included for each absorption band of each isolated nonoverlapping chromophore. The rotational strengths, transition frequencies, and polymer band shapes are determined by solving a complex eigenvalue problem.

Linear response theory of molecular interaction: Correlated Π electron systems

A many‐body theory of molecular interaction is presented for systems of nonoverlapping molecules containing delocalized Π electrons. The theory is based on a combination of LCAO MO theory and time‐dependent Hartree linear response theory. A multipole expansion of the Coulomb interaction is not employed rendering the theory applicable to large molecules. Some aspects of electron correlation are included. The infinite order result for the dispersion interaction is the change in the intermolecular correlation energy associated with ’’turning on’’ the Coulomb potential. A closed‐form infinite order expression for the intermolecular permanent moment interaction accounts for the modification of the bare Coulomb interaction by the polarizable system. Second order results that include all orders of intramolecular correlation for the dispersion and static interactions are also obtained. These are expanded in terms of the intramolecular correlation. A three‐body dispersion potential that includes all orders of intr...

Extended time dependent Hartree theory of van der Waals interaction: Inclusion of electric quadrupoles

Expressions are derived for the van der Waals interaction free energy, to infinite order, which include dipole and quadrupole interactions. The treatment is an extension of the time‐dependent Hartree approximation developed previously for dipolar interactions. The results are obtained via linear response theory. Just as in the dipolar case, the results are expressed in terms of the eigen frequencies of a normal mode matrix. In the present formulation, however, the normal modes are determined not only by electric dipolar coupling but also by coupling of electric quadrupoles with each other and with dipoles. The method is also useful in generating the perturbation terms of the free energy shift. It is found that the second order term, when applied to isotropic oscillators at zero degrees, reduces to the result derived earlier by Margenau. The nonadditive three‐body potential, derived here, reduces to the Axilrod–Teller triple dipole potential in the absence of quadrupoles. Numerical results are given for th...

Elliptical dichroism of oriented helical polymers

Abstract A linear response theory of elliptical dichroism is obtained for light propagating perpendicular to the helix axes of a system of oriented helical polymers by solving the equation of motion for the radiation fields average vector potential. A nonlinear mixture of circular and linear dichroism and birefringence is obtained.