Search results for "Hamiltonian"
showing 10 items of 662 documents
Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems
2021
In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.
Perturbations of symmetric elliptic Hamiltonians of degree four
2006
AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.
Getting discriminant functions of antibacterial activity from physicochemical and topological parameters.
2001
Linear discriminant analysis has been demonstrated to be a very useful tool in the selection and design of new drugs. Up to now we have used it through the search of a topological pattern of activity. In this work our goal is to calculate a complete set of physicochemical parameters using semiempirical (quantum chemical) calculations as well as topological indices (TIs) and try to find out any discriminant function for antibacterial activity through the combined use of both types of descriptors. The physicochemical parameters, such as heat of formation, HOMO, LUMO, dipole moment, polarizability, hyperpolarizability, PM3 generated IR vibrational frequencies, etc., were calculated using PM3 H…
Coupled-cluster theory for atoms and molecules in strong magnetic fields
2015
An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the depende…
An ab initio CI study on the rotational barrier of the allyl anion
1986
All-electron and pseudopotential non-empirical calculations have been performed on C 2v and C s (syn, anti) allyl anion conformations. Using a double-zeta valence-shell basis set within the Epstein-Nesbet definition of the unperturbed Hamiltonian, a value about 19 kcal/mol is found for the barrier to rotation of the allyl anion. This value is the theoretical value obtained with greater accuracy, and the lowest one for the rotational barrier.
High-Resolution Spectroscopy and Structure of Osmium Tetroxide. A Benchmark Study on 192OsO4
2012
Osmium tetroxide (OsO(4)) is a heavy tetrahedral molecule that constitutes a benchmark for quantum chemistry calculations. Its favorable spin statistics (due to the zero nuclear spin of oxygen atoms) is such that only A(1) and A(2) (T(d) symmetry) rovibrational levels are allowed, leading to a dense but quite easily resolvable spectrum. We reinvestigate here the ν(1)/ν(3) stretching fundamental (940-980 cm(-1)) dyad region and perform new assignments and effective Hamiltonian parameter fits for the main isotopologue ((192)OsO(4)). We also investigate the ν(2)/ν(4) bending fundamental dyad (300-360 cm(-1)) for the first time and perform a preliminary analysis. New experimental data have been…
On the approximation of the similarity-transformed Hamiltonian in single-reference and multireference coupled cluster theory
2012
Abstract We consider the recursive single commutator (RSC) approximation of the Baker–Campbell–Hausdorff expansion introduced by Yanai and Chan [T. Yanai, G.K.-L. Chan, J. Chem. Phys. 124 (2006) 194106] and apply it in order to approximate the similarity transformation of the Hamiltonian in both traditional and unitary coupled cluster theory. The equilibrium bond distance, harmonic vibrational frequency, and anharmonic constant of H2, HF, N2, CuH, and Cu2 were computed using the coupled cluster approach with single and double excitations (CCSD) and CCSD with the RSC approximation of the similarity-transformed Hamiltonian (CCSD-RSC). Our results demonstrate that the RSC approximation introdu…
Analytic second derivatives for the spin-free exact two-component theory
2011
The formulation and implementation of the spin-free (SF) exact two-component (X2c) theory at the one-electron level (SFX2c-1e) is extended in the present work to the analytic evaluation of second derivatives of the energy. In the X2c-1e scheme, the four-component one-electron Dirac Hamiltonian is block diagonalized in its matrix representation and the resulting "electrons-only" two-component Hamiltonian is then used together with untransformed two-electron interactions. The derivatives of the two-component Hamiltonian can thus be obtained by means of simple manipulations of the parent four-component Hamiltonian integrals and derivative integrals. The SF version of X2c-1e can furthermore exp…
Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian
2001
Abstract A new effective Hamiltonian is reported for the kinetic exchange between two arbitrary terms 2S A +1 Λ A and 2S B +1 Λ B that can be ground or excited in octahedrally coordinated transition metal ions. This Hamiltonian is applicable to both homo- and heterometallic clusters. For the homonuclear cluster the resonance part of the effective Hamiltonian is also presented for the case when one of the ions is excited. The operator part of the exchange Hamiltonian contains symmetry adapted products of the cubic irreducible tensors acting in orbital spaces ΛA and ΛB and scalar product of site spin operators. The parameters of the Hamiltonian are defined by the relevant intercenter transfer…
Magnetic Excitations in Polyoxometalate Clusters Observed by Inelastic Neutron Scattering: Evidence for Anisotropic Ferromagnetic Exchange Interacti…
1999
The ground-state properties of the tetranuclear Co2+ cluster [Co4(H2O)2(PW9O34)2]10- were investigated by combining specific heat, magnetic susceptibility, and magnetization measurements with a detailed inelastic neutron scattering (INS) study on a fully deuterated sample of K10[Co4(H2O)2(PW9O34)2]·22H2O. As a result of the single ion anisotropy of the octahedral Co2+, the appropriate exchange Hamiltonian of the Co4 spin cluster is anisotropic. INS turns out to be essential for the determination of energy splittings in the ground state resulting from the coupling. Besides the energy pattern, INS provides information about the wave functions of the split ground-state components of the spin c…