A. V. Scherbinin

The Lenz vector in the confined hydrogen atom problem

Abstract A general criterion for the degeneracy of states of the hydrogen atom placed in a spherical impenetrable box of radius R is formulated on the basis of the Lenz vector formalism. The reasons for the elimination of the Coulomb degeneracy typical of the conventional hydrogen atom problem and for the non-conservation of the Lenz vector are discussed. The explanation of the simultaneous degeneracy of some energy levels (e.g. 2s and 3d, 3s and 4d, etc. at R =2 au) is given.

Perturbation theory for the hydrogen atom in a spherical cavity with off-centre nucleus

The problem of a hydrogen atom in an impenetrable spherical cavity of small radius R is considered on the basis of the first-order perturbational treatment of the electron-nucleus interaction taking explicit account of the boundary condition. An approximate analytic expression is derived for the electronic energy as a function of the shift of the nucleus off the centre. The estimations obtained are in good qualitative and semiquantitative agreement with the results of the finite-difference calculations. Some general features of the energy dependences are discussed qualitatively.

Ab initio study of phosphorescent emitters based on rare-earth complexes with organic ligands for organic electroluminescent devices.

An ab initio approach is developed for calculation of low-lying excited states in Ln(3+) complexes with organic ligands. The energies of the ground and excited states are calculated using the XMCQDPT2/CASSCF approximation; the 4f electrons of the Ln(3+) ion are included in the core, and the effects of the core electrons are described by scalar quasirelativistic 4f-in-core pseudopotentials. The geometries of the complexes in the ground and triplet excited states are fully optimized at the CASSCF level, and the resulting excited states have been found to be localized on one of the ligands. The efficiency of ligand-to-lanthanide energy transfer is assessed based on the relative energies of the triplet excited states localized on the organic ligands with respect to the receiving and emitting levels of the Ln(3+) ion. It is shown that ligand relaxation in the excited state should be properly taken into account in order to adequately describe energy transfer in the complexes. It is demonstrated that the efficiency of antenna ligands for lanthanide complexes used as phosphorescent emitters in organic light-emitting devices can be reasonably predicted using the procedure suggested in this work. Hence, the best antenna ligands can be selected in silico based on theoretical calculations of ligand-localized excited energy levels.

Hidden symmetry in the confined hydrogen atom problem

The classical counterpart of the well-known quantum mechanical model of a spherically confined hydrogen atom is examined in terms of the Lenz vector, a dynamic variable featuring the conventional Kepler problem. It is shown that a conditional conservation law associated with the Lenz vector is true, in fair agreement with the corresponding quantum problem previously found to exhibit a hidden symmetry as well.

Environmental broadening of the CTTS bands: the hexaammineruthenium(II) complex in aqueous solution.

Cluster ab initio quantum chemistry approach is developed to simulate the charge-transfer-to-solvent (CTTS) absorption band and satellite ligand field bands of hexaammineruthenium(II) ion in aqueous solution. Several cluster models, including 16, 21, and 38 water molecules, are explored for this purpose. TDDFT method with long-range corrected BLYP (LC-BLYP) functional is used to obtain the vertical transition characteristics, and DFT B3LYP is used for calculation of the ground state geometry and vibrational frequencies of the solvated complex. A simple harmonic bath model is employed to estimate the absorption bandwidths and coherence decay times with the parameters taken from the quantum chemistry calculations. The present approach provides rather reasonable estimates for the CTTS band position and shape, also giving an additional insight for the mechanism of the CTTS band broadening.

Simulating the structureless emission bands of Mn2+ ions in ZnCO3 and CaCO3 matrices by means of quantum chemistry

Results from theoretical studies on the structureless luminescence spectra of Mn2+ impurity ions in matrices of calcite (CaCO3) and smithsonite (ZnCO3) are reported. The positions of the maxima and the width of the 4T1(4G) → 6A1(6S) emission bands of the indicated luminophors are calculated using a combined approach based on the periodic and cluster methods of quantum chemistry, and on well-known models of the vibrational broadening of electronic transition bands of impurity centers in crystals. The calculated parameters of the spectral bands are compared with the known experimental data and discussed in terms of the structural features of the investigated matrices and the contribution from lattice vibrations in the mechanism of broadening.

The Kirkwood–Buckingham variational method and the boundary value problems for the molecular Schrödinger equation

The approach based on the multiplicative form of a trial wave function within the framework of the variational method, initially proposed by Kirkwood and Buckingham, is shown to be an effective analytical tool in the quantum mechanical study of atoms and molecules. As an example, the elementary proof is given to the fact that the ground state energy of a molecular system placed into the box with walls of finite height goes to the corresponding eigenvalue of the Dirichlet boundary value problem when the height of the walls is growing up to infinity.

States of a hydrogen atom in an impenetrable cubic cavity

Changes in the relative positions of energy levels of a hydrogen atom placed into an impenetrable cubic cavity under both variations of the cavity size and nuclear displacements off the center alongside the fourfold symmetry axes are studied. Numerical estimates for the energies of the states corresponding to 1s, 2s, 2p, 3d states in the free atom, are performed using the collocation method for cavities with edge lengths within 1 to 6 au. Qualitative methods that may be used to analyze the changes in the atomic states in a cubic cavity under variations of its form or nuclear displacements are discussed.

On the use of multipole expansion of the Coulomb potential in quantum chemistry

Some features of the multipole expansion of the Coulomb potential V for a system of point charges are studied. It is shown that multipole expansion is convergent both locally in L2(R3) and weakly on some classes of functions. One-particle Hamiltonians Hn = H0 + Vn, where H0 is the kinetic energy operator and Vn is the n-th partial sum of the multipole expansion of V, are discussed, and the convergence of their eigenvalues to those of H = H0 + V with increasing n is proved. It is also shown that the discrete spectrum eigenfunctions of Hn converge to those of H both in L2(R3) (together with their first and second derivatives) and uniformly on R3.