The gapless energy spectrum and spin-Peierls instability of 1D Heisenberg spin systems in polymeric complexes of transition metals and hypothetical carbon allotropes.

We investigate the spin-Peierls instability of some periodic 1D Heisenberg spin systems having a gapless energy spectrum at different values of coupling J between the unit cells. Using the density-matrix renormalization group method we numerically study the dependence of critical exponents p  of spin-Peierls transition of above spin systems on the value of J. In contrast to chain systems, we find significantly non-monotonous dependence p (J) for three-legs ladder system. In the limit of weak coupling J we derive effective spin s chain Hamiltonians describing the low-energy states of the system considered by means of perturbation theory. The value of site spin s coincides with the value of the ground-state spin of the isolated unit cell of the system considered. This means that at small J values all the systems with the singlet ground state and the same half-integer value of s should have a similar critical behavior which is in agreement with our numerical study. The presence of gapped excitations inside the unit cells at small values of J should give, for our spin systems, at least one intermediate plateau in field dependence of magnetization at low temperatures. The stability of this plateau against the increase of the values of J and temperature is studied using the quantum Monte-Carlo method.

Magneto-optical response of 3d-decorated polyoxomolybdates with ε-Keggin structure.

A family of virtually isostructural tetra-capped ε-Keggin-type polyoxomolybdate(V) cluster compounds, [Mo12(V)O28(µ(2)­OH)10(µ(3)­OH)2{M(II)(H2O)3}4]·nH2O ({M4(II)Mo12(V)}, M = Ni, Co), exhibits magnetic-field-dependent optical response in their electronic absorption spectra in the 0­33 T range. On the basis of Effective Hamiltonian Crystal Field calculations, we find that the observed field-induced decrease in reflectance of these compounds can be related to the formally spin-forbidden on-site d­d excitations. We tentatively position the observed effect among other known magneto-optical effects and predict that similar features may be found for other {M49(II)Mo12(V)} analogues.

Low-temperature structure anomalies in CuNCN. Manifestations of RVB phase transitions?

We propose a new frustrated Heisenberg antiferromagnetic model with spatially anisotropic exchange parameters Jc, Ja, and Jac, extending along the c, a, and a ± c (c-a-ca model) lattice directions, and apply it to describe the fascinating physics of copper carbodiimide, CuNCN, assuming the resonating valence bond (RVB) type of its phases. This explains within a unified picture the intriguing absence of magnetic order in CuNCN. We further present a parameters-temperature phase diagram of the c-a-ca-RVB model in the high-temperature approximation. Eight different phases including Curie and Pauli paramagnets (respectively, in disordered and 1D- or Q1D-RVB phases) and (pseudo)gapped (quasi-Arrhenius) paramagnets (2D-RVB phases) are possible. By adding magnetostriction and elastic terms to the model, we derive possible structural manifestations of RVB phase transitions. Assuming a sequence of RVB phase transitions to occur in CuNCN with decreasing temperature, several anomalies observed in the temperature course of the lattice constants are explained.

Unconventional magnetism in a nitrogen-containing analog of cupric oxide.

We have investigated the magnetic properties of CuNCN, the first nitrogen-based analog of cupric oxide CuO. Our muon-spin relaxation, nuclear magnetic resonance, and electron-spin resonance studies reveal that classical magnetic ordering is absent down to the lowest temperatures. However, a large enhancement of spin correlations and an unexpected inhomogeneous magnetism have been observed below 80 K. We attribute this to a peculiar fragility of the electronic state against weak perturbations due to geometrical frustration, which selects between competing spin-liquid and more conventional frozen states.

Multipole model for the electron group functions method.

Electron groups provide a natural way to introduce local concepts into quantum chemistry, and the wave functions based on the group products can be considered as a framework for constructing efficient computational methods in terms of "observable" parts of molecular systems. The elements of the group wave functions (electronic structure variables) can be optimized by requiring the number of operations proportional to the size of the molecule. This directly leads to computational methods linearly scaling for large molecular systems. In the present work we consider a particular case of such a wave function implemented for the semiempirical NDDO Hamiltonian. The electron groups are expressed in terms of optimized atomic (hybrid) orbitals with chemical bonds described by geminals and the delocalized groups described by Slater determinants (with or without spin restriction). This scheme is very fast by itself but its speed is considerably limited by the computations of the interatomic Coulomb interactions. Here we develop a consistent method based on group functions which uses the multipole scheme for interatomic interactions. The explicit usage of the atomic multipoles makes the method extremely fast, although the numerical efficiency is largely achieved due to the local character of the electron groups involved. We discuss numerical characteristics of the new method as well as its possible parametrization. We apply this method to study dodecahedral water clusters with hydrogen fluoride substitution and base the analysis on the exhaustive calculation of all symmetry-independent hydrogen-bond networks.

Transferability of parameters of strictly local geminals' wave function and possibility of sequential derivation of molecular mechanics.

The problem of substantiation of molecular mechanics (MM) remains actual due to growing popularity of hybrid quantum/classical (QM/MM) schemes. Recently proposed deductive molecular mechanics (DMM) seems to be a natural tool to derive mechanistic models of molecular energy (classical force fields) from a suitable quantum mechanical (QM) description of molecular structure. It is based on an assumption that the trial wave function underlying the MM description is one of the antisymmetrized product of strictly local geminals (SLG). A proof of transferability of electronic structure parameters (ESPs) in this approximation is an essential component of a logical framework for the transition from the QM to an MM description because it allows constructing expressions for potential energy surfaces by proper consideration of the response of the ESPs to the variations of geometry parameters. In the present article the ESPs defining density matrix elements and basis one-electron states (hybrid orbitals-HOs) in the SLG approximation are formally considered. The transferability of the density matrix elements with respect to the parameters of molecular electronic structure and the linear response relations for the HOs are proven to take place under very nonrestrictive conditions. Special attention is paid to numerical estimates of the ESPs' features giving an "experimental" support to approximate expressions for the molecular energy.

Efficient multipole model and linear scaling of NDDO-based methods.

Fast growth of computational costs with that of the system's size is a bottleneck for the applications of traditional methods of quantum chemistry to polyatomic molecular systems. This problem is addressed by the development of linear (or almost linear) scaling methods. In the semiempirical domain, it is typically achieved by a series of approximations to the self-consistent field (SCF) solution. By contrast, we propose a route to linear scalability by modifying the trial wave function itself. Our approach is based on variationally determined strictly local one-electron states and a geminal representation of chemical bonds and lone pairs. A serious obstacle previously faced on this route were the numerous transformations of the two-center repulsion integrals characteristic for the neglect of diatomic differential overlap (NDDO) methods. We pass it by replacing the fictitious charge configurations usual for the NDDO scheme by atomic multipoles interacting through semiempirical potentials. It ensures invariance of these integrals and improves the computational efficiency of the whole method. We discuss possible schemes for evaluating the integrals as well as their numerical values. The method proposed is implemented for the most popular modified neglect of diatomic overlap (MNDO), Austin model 1 (AM1), and PM3 parametrization schemes of the NDDO family. Our calculations involving well-justified cutoff procedures for molecular interactions unequivocally show that the proposed scheme provides almost linear scaling of computational costs with the system's size. The numerical results on molecular properties certify that our method is superior with respect to its SCF-based ancestors.

Low- and high-spin iron (II) complexes studied by effective crystal field method combined with molecular mechanics.

A computational method targeted to Werner-type complexes is developed on the basis of quantum mechanical effective Hamiltonian crystal field (EHCF) methodology (previously proposed for describing electronic structure of transition metal complexes) combined with the Gillespie-Kepert version of molecular mechanics (MM). It is a special version of the hybrid quantum/MM approach. The MM part is responsible for representing the whole molecule, including ligand atoms and metal ion coordination sphere, but leaving out the effects of the d-shell. The quantum mechanical EHCF part is limited to the metal ion d-shell. The method reproduces with reasonable accuracy geometry and spin states of the Fe(II) complexes with monodentate and polydentate aromatic ligands with nitrogen donor atoms. In this setting a single set of MM parameters set is shown to be sufficient for handling all spin states of the complexes under consideration.