The near-UV absorption spectra of barnase double-point mutants are calculated using a combination of molecular dynamics and ab initio techniques. The atoms of the fluorescent probes are placed in a cloud of point charges, generated by molecular dynamics simulations. Ab initio calculations (CASPT2) are performed on these systems. Three molecular dynamics packages are compared-Amber5.0, CHARMMc27b1, and GROMOS96-using indole as the fluorescent probe. It was found that calculated absorption spectra reproduce experimental values very well, provided detailed charge cloud descriptions are included. These calculations further sustain the hypothesis that different tryptophan rotamers can be present in proteins. Molecular dynamics calculations of the double-point mutants also point to the structural effect of counter ions.

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic with the dihedral group D N . In this paper group-theoretical 'parameters' of such groups are determined, especially decompositions of transitive representations into irreducible ones and double cosets. These results are necessary to construct matrix elements of any operator commuting with G in an efficient way. The approach proposed can be usefull in many branches of physics, but here it is applied to finite spin systems, which serve as models for mesoscopic magnets.

Abstract. Finite spin models, applicable to investigations of mesoscopic rings, give rise to eigenproblems of very large dimensions. Efficient, and as exact as possible, solutions of such eigenproblems are very difficult. A method leading to block diagonalization of Hamiltonian matrix is proposed in this paper. For a given symmetry group of a Heisenberg Hamiltonian commuting with the total spin projection (i.e. with the total magnetization being a good quantum number) appropriate combinatorial and group-theoretical structures (partitions, orbits, stabilizers etc.) are introduced and briefly discussed. Generation of these structures can be performed by means of algorithms being modifications of standard ones. Main ideas are presented in this paper, whereas the actual form of algorithms will be discussed elsewhere.

The spin correlations ω z r , r = 1, 2, 3, and the probability pN of finding a system in the Néel state for the antiferromagnetic ring Fe III 6 (the so-called 'small ferric wheel') are calculated. States with magnetization M = 0, total spin 0 ≤ S ≤ 15 and labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D6 are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S-multiplet. Taking into account the Clebsch-Gordan coefficients for coupling total spins of sublattices (SA = SB = 15 2 ) the global Néel probability p * N can be determined. Dependencies of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined pN(S) etc. for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results are calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 thousands basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S = 0). The largest eigenproblem has to be solved for S = 4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm efficiency and usefulness of such an approach, so it is briefly discussed here.