On the theory of the migration of incoherent excitons

The probability of a localized exciton jump between molecules with allowance for exciton-exciton interaction is obtained in the adiabatic approximation. Above the Debye temperature, an analytic dependence of this probability on the exciton-exciton interaction is found and the role of the interaction in the annihilation process is discussed.     

On the application of accelerated molecular dynamics to liquid water simulations

Our group recently proposed a robust bias potential function that can be used in an efficient all-atom accelerated molecular dynamics (MD) approach to simulate the transition of high energy barriers without any advance knowledge of the potential-energy landscape. The main idea is to modify the potential-energy surface by adding a bias, or boost, potential in regions close to the local minima, such that all transitions rates are increased. By applying the accelerated MD simulation method to liquid water, we observed that this new simulation technique accelerates the molecular motion without losing its microscopic structure and equilibrium properties. Our results showed that the application of a small boost energy on the potential-energy surface significantly reduces the statistical inefficiency of the simulation while keeping all the other calculated properties unchanged. On the other hand, although aggressive acceleration of the dynamics simulation increases the self-diffusion coefficient of water molecules greatly and dramatically reduces the correlation time of the simulation, configurations representative of the true structure of liquid water are poorly sampled. Our results also showed the strength and robustness of this simulation technique, which confirm this approach as a very useful and promising tool to extend the time scale of the all-atom simulations of biological system with explicit solvent models. However, we should keep in mind that there is a compromise between the strength of the boost applied in the simulation and the reproduction of the ensemble average properties.     

Sequence-adapted molecular tensors: Algebraic methods and application to crystal field theory

Tensorial sets adapted to sequences of finite subgroups are applied to the crystal field problem, and a general method for generating sequence-adapted molecular tensors using finite group algebra is formulated. All subgroup sequences of the abstract finite group G(24), isomorphic to the octahedral, O, tetrahedral, T_d, and symmetric, S(4), groups are tabulated with explicit isomorphisms provided. The sequences fall into eight equivalence classes. A catalog of irreducible representations of G(24) adapted to a member of each of the eight sequence classes is given together with the transformations which generate representations adapted to all other sequences. With this data it is possible to systematically generate tensorial sets adapted to any sequence of a realization of G(24). Unitary transformations which adapt conventional forms of first- and second-rank irreducible tensorial sets of the rotation group to the eight sequences of the octahedral group are provided. Forms suitable for use with magnetic fields are included. The problem of a d¹ ion in a trigonal crystal field is treated with sequence-adapted molecular tensors, and the utility of different sequences for descent in symmetry is discussed.     

Utilization of deformations in molecular quantum chemistry and application to density functional theory

The aim of this article is to present in a way accessible to most quantum chemists a general mathematical method which consists in deforming wave functions and density functions (in the spirit of the local scaling transformation). This deformation method allows us to obtain several new results, including a characterization of the set of wave functions that have the same given density function (which gives a new insight on a result of G. Zumbach and K. Maschke, Phys. Rev. A 28 , 544 (1983)) and an N-representability result where symmetry is taken into account. We also propose new theoretical ways to generate approximations of the exact density functional and give a numerical example. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 221–231, 1998     

From the Periphery: the genesis of Eugene P. Wigner's application of group theory to quantum mechanics

This paper traces the origins of Eugene Wigner's pioneering application of group theory to quantum physics to his early work in chemistry and crystallography. In the early 1920s, crystallography was the only discipline in which symmetry groups were routinely used. Wigner's early training in chemistry, and his work in crystallography with Herman Mark and Karl Weissenberg at the Kaiser Wilhelm institute for fiber research in Berlin exposed him to conceptual tools which were absent from the pedagogy available to physicists for many years to come. This both enabled and pushed him to apply the group theoretic approach to quantum physics. It took many years for the approach first introduced by Wigner in the 1920s – and whose reception by the physicists was initially problematical – to assume the pivotal place it now holds in physical theory and education. This is but one example that attests to the historic contribution made by the periphery in initiating new types of thought-perspectives and scientific careers.     

Anderson''s localization of molecular excitons in substitutionally disordered systems

We present clear evidence for the presence of Anderson's localization in molecular solids. Diagonal and off-diagonal disorder is introduced and controlled by substitutionally disordering the lattice at different temperatures. Optical and optically-detected magnetic resonance spectroscopy have been used to directly obtain the resonance interactions, the inhomogeneous site-energy fluctuations, and the threshold for Anderson's transition. The results on the two-dimensional lattice when compared with quasi-one-dimensional systems indicate that cross chain interactions and phonon-assisted processes are important in determining the nature of extended states in disordered systems.     

The nature of singlet excitons in oligoacene molecular crystals

A theory for polarized absorption in crystalline oligoacenes is presented, which includes Frenkel exciton coupling, the coupling between Frenkel and charge-transfer (CT) excitons, and the coupling of all neutral and ionic excited states to the dominant ring-breathing vibrational mode. For tetracene, spectra calculated using all Frenkel couplings among the five lowest energy molecular singlet states predict a Davydov splitting (DS) of the lowest energy (0-0) vibronic band of only -32 cm(-1), far smaller than the measured value of 631 cm(-1) and of the wrong sign-a negative sign indicating that the polarizations of the lower and upper Davydov components are reversed from experiment. Inclusion of Frenkel-CT coupling dramatically improves the agreement with experiment, yielding a 0-0 DS of 601 cm(-1) and a nearly quantitative reproduction of the relative spectral intensities of the 0-n vibronic components. Our analysis also shows that CT mixing increases with the size of the oligoacenes. We discuss the implications of these results on exciton dissociation and transport.     

Application of the group function theory to infinite systems

We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill‐defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A “linked‐AD” theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long‐range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 511–534, 2000     

New generation of semiempirical methods of molecular modeling based on the theory of group functions

The semiempirical methods of modeling the molecular systems using the group function approximation for electronic structure calculations have been used by the author for many years. The review discusses the general structure of the semiempirical method that uses the group functions and the results obtained by the particular methods, namely, the crystal field effective Hamiltonian method designed for systems containing transition metal ions and methods based on the strictly local geminal approximation designed for modeling the “organic” molecules.     

On the separation of motions in the theory of polyatomic molecular spectra

A method has been suggested for the separation of rotational and vibrational motions of nuclei in polyatomic molecules. The method is based on the introduction of the angular velocity vector associated with the kinetic moment and provides the complete separation of motions in the case of arbitrary molecule deformations. The method requires no a priori assumptions on vibrational amplitudes.     

Pseudospectral approach to relativistic molecular theory

The efficient relativistic Dirac-Hartree-Fock (DHF) and Dirac-Kohn-Sham (DKS) methods are proposed by an application of the pseudospectral (PS) approach. The present PS-DHF/DKS method is a relativistic extension of the PS-HF/KS method of Friesner, though we aim at higher numerical accuracy by elimination of superfluous arbitrariness. The relativistic PS-DHF/DKS method is implemented into our REL4D programs. Several PS applications to molecular systems show that the relativistic PS-DHF/DKS approach is more efficient than the traditional approach without a loss of accuracy. The present PS-DKS method successfully assigns and predicts the photoelectron spectra of hexacarbonyl complexes of tungsten and seaborgium theoretically.     

On the applicability of multireference second-order perturbation theory to study weak magnetic coupling in molecular complexes

The performance of multiconfigurational second-order perturbation techniques is established for the calculation of small magnetic couplings in heterobinuclear complexes. Whereas CASPT2 gives satisfactory results for relatively strong magnetic couplings, the method shows important deviations from the expected Heisenberg spectrum for couplings smaller than 15-20 cm(-1). The standard choice of the zeroth-order CASPT2 Hamiltonian is compared to alternative definitions published in the literature and the stability of the results is tested against increasing level shifts. Furthermore, we compare CASPT2 with an alternative implementation of multiconfigurational perturbation theory, namely NEVPT2 and with variational calculations based on the difference dedicated CI technique.     

Interaction of charge transfer excitons with phonons in molecular crystals

Interaction of charge transfer excitons with phonons due to modulation of the Coulomb electron-hole attraction by lattice oscillations is considered. Such interaction leads in some cases to self-trapping of CT excitons and, as a result, to the hopping character of their migration in the crystal. Spectra of optical absorption with the excitation of these states take the form of broad gaussian curves.