Calculation of the Non-Bonding Molecular Orbitals in the Hulckel Theory

A method is given to obtain all NBMO\u27s for both alternant and nonalternant aromatic hydrocarbons. In addition few theorems are derived which can be used to deduce some (or all) of the NBMO\u27s directly from the graph of the molecule

Splitting of the Configuration Interaction Space Xn into Two Complementary Subspaces

The confi.g:uration interaction space Xn generated by n particles moving over 2n orbitals is considered. The formalism of the molecular orbital resonance theoil:y {MORT) a,pproach is used. H is shown tha.t the space Xn can be split into SIUJbspaces Xn+ and Xn- so that »e1ementary« one-particle opera.tors connect either the stJartes contained in ithe same subspace, oil: they conn:ec.t the sitates contained in different subsipaces. In pa·rticular, each state qt+ E Xn+ atlld each state qt- E Xn- has a uni:form charge density distribution over all 2n oirbitals, and vanishing bond orders between orbi1tals of the same parity. As a sirrn,ple consequence the pairing theorem results. To be »alternant-liike« .is thus shown to be the property of whole spaces Xn + atlld Xn- , rather ithan the property 01f paxticulair eigenstates. The coinnectiioin wilt

Doping-induced quantum cross-over in Er2_2Ti2−x_{2-x}Snx_xO7_7

We present the results of the investigation of magnetic properties of the Er$_2$Ti$_{2-x}$Sn$_x$O$_7$ series. For small doping values the ordering temperature decreases linearly with $x$ while the moment configuration remains the same as in the $x = 0$ parent compound. Around $x = 1.7$ doping level we observe a change in the behavior, where the ordering temperature starts to increase and new magnetic Bragg peaks appear. For the first time we present evidence of a long-range order (LRO) in Er$_2$Sn$_2$O$_7$ ($x = 2.0$) below $T_N = 130$ mK. It is revealed that the moment configuration corresponds to a Palmer-Chalker type with a value of the magnetic moment significantly renormalized compared to $x = 0$. We discuss our results in the framework of a possible quantum phase transition occurring close to $x = 1.7$.Comment: accepted in PRB Rapi

On the Pairwise Nonorthogonality Problem in Quantum Chemistry

It is shown that, starting from a set of local hybrid orbitals if>; (i = 1, . .. n) one can construct pairwise nonorthogonal set of functions Xi (i = 1, ... n) with the following feature calculated by employing maximum overlap criterion or by max,imizim. g the average distance between the centroids of charge of the electronic pairs. The use of the pairwise nonorthogonal functions is advantageous in semiempirical methods since it minimizes the error introduced by the neglect of the many-center electron repulsion integrals

On Additivity of Heats of Atomization of Benzenoid Hydrocarbons

An additivity scheme, based on Clar\u27s formulae, is proposed for calculating heats of atomization of benzenoid hydrocarbons: Comparison between the results obtained by this scheme, by the semiempirical SCF MO model, and experimental findings is good. This satisfactory agreement, thus, presents independent support for Clar\u27s notion of isolated Jt sextets and migrating sextets

On the Topological Spectra of Composite Molecular Systems

It has been shown that topological spectrum of some large molecules comprises the complete set of eigenvalues of the topological matrix of some of their constituting fragments. Several relationships between the coefficients of the fragmental eigenvectors and those of the composite system have been derived. Some sufficient conditions that a system comprise a spectrum of its parts have been found and their use illustrated

On the Topological Spectra of Composite Molecular Systems

It has been shown that topological spectrum of some large molecules comprises the complete set of eigenvalues of the topological matrix of some of their constituting fragments. Several relationships between the coefficients of the fragmental eigenvectors and those of the composite system have been derived. Some sufficient conditions that a system comprise a spectrum of its parts have been found and their use illustrated

Theoretical Studies on Radialenes and Related Molecules

For certain classes of molecules it is possible to obtain a general solution ·of the Ruckel problem, i.e. to derive expressions for the orbital energy, orbital coefficients, total n-electron energy, etc. in a closed analytical form1-5• General solutions are important because a large amount of numerical labour can be saved. Besides, they show the dependence of HMO quantities on the molecular topology, which has been recently investigated by various authors

Calculation of the Non-Bonding Molecular Orbitals in the Hulckel Theory

A method is given to obtain all NBMO\u27s for both alternant and nonalternant aromatic hydrocarbons. In addition few theorems are derived which can be used to deduce some (or all) of the NBMO\u27s directly from the graph of the molecule

Two-step transition in a magnetoelectric ferrimagnet Cu2OSeO3

We report a detailed single crystal investigation of a magnetoelectric ferrimagnet Cu2OSeO3 using dc magnetization and ac susceptibility along the three principal directions [100], [110] and [111]. We have observed that in small magnetic fields two magnetic transitions occur, one at Tc = 57 K and the second one at TN = 58 K. At Tc the non-linear susceptibility reveals the emergence of the ferromagnetic component and below Tc the magnetization measurements show the splitting between field-cooled and zero-field-cooled regimes. Above 1000 Oe the magnetization saturates and the system is in a single domain state. The temperature dependence of the saturation below Tc can be well described by m(T) = m(0)[1 - (T/Tc)^2]^{\beta}, with m(0) = 0.56 (mu)B/Cu, corresponding to the 3-up-1-down configuration. The dielectric constant measured on a thin single crystal shows a systematic deviation below the transition, indicating an intrinsic magnetoelectric effect.Comment: accepted for publication in PR