Quantum Chemistry of Excited State: Tamm-Dankoff Approximation with Correlated Wave Functions

A simple derivation of the general equations of the Tamm-Dankoff approximation (TDA) is presented using the equation-of-motion technique to describe electronic excitations in molecules. It is emphasized that the performance of this method strongly depends on the accuracy of the reference (ground) state. Though the Hartree-Fock ground state is commonly applied, the \u27all-single CI\u27 (CIS) method based on it is not too reliable. On the other hand, if the ground state is described by sophisticated wave functions like CISD or a coupled cluster ansatz, the TDA equations become quite complicated and may even turn inconsistent. We advocate the use of geminal type ground state wave functions, which, if the strong orthogonality condition is utilized, provide an efficient starting point, being not only highly correlated but also very transparent. Fully consistent TDA equations are derived for strongly orthogonal geminals, which can be of great help in the interpretation of molecular spectra in terms of local contributions and chromophores

Conditions for describing triplet states in reduced density matrix functional theory

We consider necessary conditions for the one-body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied

AUTOMATIC TEST GENERATION BASED ON CONSTRAINTS

It seems to be a very hard task to enhance the properties of widespreadly used automatic test pattern generation algorithms. Experiences show that achievements are sometimes not worth the effort. In the authors' opinion this fact stems from the basically 'algorithm oriented' nature of research made in the past. A new experimental framework is presented for the problem, considering network representation and search control algorithms as equally important parts. The network is represented by object- oriented data-flow networks, the search control algorithm is based on constraint satisfaction, and a special kind of dependency directed backtracking which we call constraint slackening. Similar methods were proved to be very useful in automatic system diagnosis by DAVIS (1985) and others, although have not been introduced to testing yet. This paper summarises the basic notions of constraint satisfaction, the potential advantages of using it for building test generation systems, and shows implementational details of a test generation system, based on constraints. Experiences of the run-time tests show that constraint-based test generation can be highly efficient

Structure of Fermionic Density Matrices: Complete N-representability Conditions

We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known conditions, while rigorous, were incomplete. Here we derive a hierarchy of constraints built upon (i) the bipolar theorem and (ii) tensor decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2, known classical conditions, and new conditions appear naturally. Subsets of the conditions are amenable to polynomial-time computations of strongly correlated systems

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Performance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li2, BH, H2O, and CH2O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li2, BH, and H2O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long- and short-range terms and employing density functionals to treat the latter is presented

Quantum Chemistry of Excited State: Tamm-Dankoff Approximation with Correlated Wave Functions

A simple derivation of the general equations of the Tamm-Dankoff approximation (TDA) is presented using the equation-of-motion technique to describe electronic excitations in molecules. It is emphasized that the performance of this method strongly depends on the accuracy of the reference (ground) state. Though the Hartree-Fock ground state is commonly applied, the \u27all-single CI\u27 (CIS) method based on it is not too reliable. On the other hand, if the ground state is described by sophisticated wave functions like CISD or a coupled cluster ansatz, the TDA equations become quite complicated and may even turn inconsistent. We advocate the use of geminal type ground state wave functions, which, if the strong orthogonality condition is utilized, provide an efficient starting point, being not only highly correlated but also very transparent. Fully consistent TDA equations are derived for strongly orthogonal geminals, which can be of great help in the interpretation of molecular spectra in terms of local contributions and chromophores

Doping Effects and Electronic States in C60-Polymers

Band structures of C60-polymers are studied changing conjugation conditions and the electron number. We use a Su-Schrieffer-Heeger type semiempirical model. In the neutral C60-polymer, electronic structures change among direct-gap insulator and the metal, depending on the degree of conjugations. The C60-polymer doped with one electron per one molecule is always a metal. The energy difference between the highest-occupied state and the lowest-unoccupied state of the neutral system becomes smaller upon doping owing to the polaron effects. The C60-polymer doped with two electrons per one C60 changes from an indirect-gap insulator to the direct-gap insulator, as the conjugations become stronger.Comment: to be published in Chem. Phys. Let

A zenei észlelés fejlettségének vizsgálata hagyományos és számítógépes tesztfelvétellel

Tanulmányunkban a zenei észlelés fejlettségét vizsgáltuk az általános iskola első évfolyamán. Célunk két eltérő adatfelvételi mód, a papír-ceruza alapú (PP) és a számítógépes tesztelés (CB) összevetése, melyhez korábbi, papír-ceruza alapú tesztünket adaptáltuk online, számítógépes felületre. Papír-ceruza alapon 130, számítógépes felületen pedig 155 tanuló vett részt a vizsgálatban. Eredményeink alapján mindkét mérőeszköz megbízhatósága megfelelő, a reliabilitásmutatók között a teljes tesztre vonatkozóan nincs szignifikáns különbség. A két teszt esetében kapott faktorstruktúrák összevethetőek, a hangmagasság észleléséhez és az időbeli feldolgozáshoz kapcsolódó készségek szerinti faktorok különíthetőek el. A zenei észlelés általános fejlettsége szerint azonban a két tesztváltozat között szignifikáns különbséget kaptunk, a papír-ceruza teszt alapján kimutatott fejlettség 8%p-al nagyobb (PP=58%p; CB=50%p). Kutatásunkat első lépésnek tekintjük, eredményeink alapján további, nagyobb mintán és magasabb évfolyamokra is kiterjedő kutatások szükségesek