Facultat de Cièncieshttp://hdl.handle.net/10256.1/13132014-07-25T07:04:13Z2014-07-25T07:04:13ZClosingSolà i Puig, Miquelhttp://hdl.handle.net/10256.1/17382011-10-17T10:49:40Z2010-07-08T00:00:00ZClosing
Solà i Puig, Miquel
Closing of IX Girona Seminar: Electron Density, Density Matrices, and Density Functional Theory, dedicated to Prof. Ramon Carbó-Dorca on occasion of his 70th birthday
2010-07-08T00:00:00ZAromaticity and the electron localization function, ELFFuentealba, Patriciohttp://hdl.handle.net/10256.1/17372011-10-17T10:18:20Z2010-07-08T00:00:00ZAromaticity and the electron localization function, ELF
Fuentealba, Patricio
It will be shown that the Electron Localization Function, ELF, can also be used to study the delocalization and aromatic character of a diversity of molecules. Although the analysis of the total ELF
does not provide clear information about aromaticity, the separation of the function on its σ and π parts yields indeed valuable information about it. Moreover, it is possible to construct a quantitative scale of aromaticity. It is also shown that the use of the ELF to understand aromaticity is complementary to other methodologies. Applications to organic and inorganic molecules and atomic clusters demonstrate the capability of the method and the possibility of distinguish between σ , π , δ… aromaticity
2010-07-08T00:00:00ZSpin-coupled descriptions of organic reactivityCooper, Davidhttp://hdl.handle.net/10256.1/17362011-10-17T10:01:00Z2010-07-08T00:00:00ZSpin-coupled descriptions of organic reactivity
Cooper, David
Valence bond theory has undergone something of a resurgence in chemistry over the last few decades, with a key role being played by so-called modern valence bond approaches such as spin-coupled theory. Given that spin-coupled theory uses the most general wavefunction based on a single orbital product, it arguably represents the highest level of theory at which one can obtain such models directly, thereby combining useful accuracy with highly visual descriptions of correlated electronic structure. We survey recent applications of spin-coupled theory to the electronic rearrangements associated with the bondbreaking and bond-formation processes along the minimum energy paths in organic chemical reactions
2010-07-08T00:00:00ZSpin component scaling in multiconfiguration perturbation theorySzabados, Agneshttp://hdl.handle.net/10256.1/17352011-10-17T09:46:17Z2010-07-08T00:00:00ZSpin component scaling in multiconfiguration perturbation theory
Szabados, Agnes
We investigate a term-by-term scaling of the second order energy correction obtained by perturbation theory (PT) based on a multiconfiguration wavefunction. The total second order correction is decomposed into several terms, based on the level and spin pattern of the excitations. In particular, same spin and different spin double excitations are grouped separately in the spirit of spin component scaling (SeS). Identification of the excitation
level is facilitated by the pivot determinant underlying the multiconfiguration PT framework. Scaling factors of the individual terms are determined from the stationary condition of the total energy calculated up to order three. In the single reference framework this procedure has been shown to result scaling factors similar to those applied in Grimme's
SeS-M011er-Plesset method. Several decomposition schemes are tested numerically on the example of bond dissociation profiles. We conclude, that the success of spin component scaling at around equilibrium geometries is not right away transferable to the entire potential surface, even if adopting a multireference based PT formulation
2010-07-08T00:00:00ZPosmom: the unobserved observableGill, Peterhttp://hdl.handle.net/10256.1/17342011-10-17T09:39:16Z2010-07-08T00:00:00ZPosmom: the unobserved observable
Gill, Peter
The position-momentum dot product (‘posmom’) s = r.p of a particle is a quantum mechanical observable and we have recently shown that its probability density S(s) can be computed efficiently from the positionspace wavefunction ψ(r) of a particle. In this lecture, I will show how the posmom density is related to the position density ρ(r) and the momentum density Π(p) and I will argue that S(s) yields insight into the nature of electronic trajectories. Finally, I will propose that electron posmometry can potentially provide information that is inaccessible from conventional diffraction or momentum methods
2010-07-08T00:00:00ZUnexpected features of relativistic modelsKarwowski, Jacekhttp://hdl.handle.net/10256.1/17332011-10-17T11:17:59Z2010-07-08T00:00:00ZUnexpected features of relativistic models
Karwowski, Jacek
Several unexpected properties of the Dirac equation, related to its multi-component structure and unboundedness from below of the Dirac Hamiltonian are discussed. In particular, a pathological behaviour of an exact density functional derived from either Dirac or Levy-Leblond equation is presented. For a oneelectron atom, as one should expect, the variational minimum of this functional gives the exact ground state energy and corresponds to the correct density. However, the same minimum is also reached by an infinite set of densities which do not correspond to the exact wave-function. Some of the wave-functions corresponding to the correct minimum are orthogonal to the exact one. It also appears that imposing the correct boundary conditions does not remove the fake solutions. As it is known, the two-electron Dirac-Coulomb equation does not have square-integrable solutions if the interaction term is present in the Hamiltonian. As a result, all the states of two-electron atoms, including the ground states are, from the formal point of view, auto-ionizing and should be treated using theoretical methods appropriate for the description of resonances. Some consequences of this facts are discussed. Transformations of the Dirac equation in the spinor space supply another degree of freedom in structuring methods of solving this equation. It appears that some non-standard representations of the Dirac equation may be more convenient in numerical applications and result in more stable variational procedures. Several examples are discussed
2010-07-08T00:00:00ZAnharmonicity as a possible explenation of the Eigen-Zundel dilema in the IR spectrum of H+(H2O)21Torrent Sucarrat, Miquelhttp://hdl.handle.net/10256.1/17322011-10-17T10:49:37Z2010-07-08T00:00:00ZAnharmonicity as a possible explenation of the Eigen-Zundel dilema in the IR spectrum of H+(H2O)21
Torrent Sucarrat, Miquel
The acid-base reaction is one of the most fundamental processes in solution and the protonated water clusters play an important role in many chemical and biological aspects. There are mainly two theories about the location of the proton in the water clusters. In the Eigen form the proton is strongly bound to a single bond (H3O+), while in the Zundel form2 lies midway between two water molecules (H2OH+-H2O). The H+(H2O)21 cluster shows an exceptional stability and it is kwon as the “magic number” in the mass distribution of H+(H2O)n.3 Theoretical calculations predicts for the H+(H2O)21 cluster an Eigen model with H3O+ on the surface of the cage.Very recently, Miyazaki et al. and Shin et al. were capable to isolate the protonated water clusters H+(H2O)n with n=6 to 27 in gas phase and measure their IR spectra from 2000 to 4000 cm-1, allowing the experimental characterisation of their Zundel and Eigen nature. They confirmed that the structure of H+(H2O)21 consists a pentagonal dodecahedra cage with an internal water. However, these studies could not determine whether the hydronium ion sits in the interior or on the surface of the water cage. In addition, the experimental spectra don’t show the characteristic intense and shifted O-H stretching vibration for the isolated H3O+ in the their IR spectra of H+(H2O)21 from 2000 to 4000 cm-1. Then, they could not determine whether the Eigen or the Zundel is the correct model for the H+(H2O)21 system. In these studies, it was pointing out the effect of the temperature and the possible contributions from more than one structural isomer of a given cluster size to explain the discrepancy between theoretical and experimental results. In the present work we present a complete different picture of this problem. We calculate the infrared anharmonic spectra of the H+(H2O)21 with the hydronium ion sits in the interior and on the surface of the water cage. We observe that the O-H stretching vibration for the isolated H3O+ can have red-shifts larger than 500 cm-1. The anharmonic effects play a crucial role to characterize the IR spectra of the protonated water clusters and our calculations indicate that the analysis of the IR spectra in the region below 2000 cm-1 can become crucial for the Eigen Zundel dilemma of H+(H2O)21
2010-07-08T00:00:00ZExplicitly correlated F12 methods using CUSP conditionsTen-no, Seiichirohttp://hdl.handle.net/10256.1/17312011-10-17T11:36:56Z2010-07-08T00:00:00ZExplicitly correlated F12 methods using CUSP conditions
Ten-no, Seiichiro
F12 methods based on the Slater-type geminal along with (complementary) auxiliary basis set ((C)ABS) or numerical quadratures (QD) for many-electron integrals lead to greatly improved
convergence of correlation energies. Moreover the use of the s- and p-wave cusp conditions for geminal amplitudes directly (SP-Ansatz) leads to numerically stable and computationally efficient methods. The SP-Ansatz is somethimes called as fixed amplitudes or diagonal orbital invariant Ansatz. We will discuss MP2-F12, CCSD(T)(F12) for the ground state energies, and several EOM-CCSD(F12) methods for various energy differences using cusp conditions
2010-07-08T00:00:00ZWhat ab-initio Quantum Chemistry (AIQC) and Density Functional Theory (DFT) can learn from each otherKutzelnigg, Wernerhttp://hdl.handle.net/10256.1/17302011-10-17T11:17:27Z2010-07-08T00:00:00ZWhat ab-initio Quantum Chemistry (AIQC) and Density Functional Theory (DFT) can learn from each other
Kutzelnigg, Werner
Starting from the common origin of AIQC and DFT, differences between AIQC and DFT are analyzed. The respective advantages and drawbacks of the two classes of methods are pointed out. A chain of approximations is presented that starts from genuine DFT, where the entire internal energy is treated as an unknown functional of the density, via Kohn-Sham type theories, orbital functional theories, and density matrix functional theory to a rigorous n-electron theory. On this way the dependence on an unknown functional is gradually reduced, while the information content of the parametrization of the state is increased. Particular attention is payed to formulations of the n-electron problem in terms of the 2-particle density matrix or rather the one-particle density matrix and the two-particle cumulant
2010-07-08T00:00:00ZDescribing dissociation in variational second order density matrix theoryVan Aggelen, Helenhttp://hdl.handle.net/10256.1/17292011-10-17T11:02:48Z2010-07-08T00:00:00ZDescribing dissociation in variational second order density matrix theory
Van Aggelen, Helen
A correct description of dissociating bonds is even more challenging to methods based on the density or first or second order density matrices than to wave function based techniques. Density and density matrix based techniques typically yield dissociated states with fractional charges instead of correct integer charges. Such non-physical fractionally charged dissociated states also occur in variational second order density matrix theory[1] under the necessary but not sufficient P-, Q- and G-condition for Nrepresentability. Additional N-representability constraints are needed to correct them. To this end, we introduced linear constraints on the energy of atomic subspaces in the molecule. This work focuses on the implementation of such subspace constraints, more specifically on the identification of the tightest set of subspace constraints, their scale-up to bigger molecules and their relationship to size-consistency. These issues are discussed in relation to the potential energy surface of the F3 - ion. First of all, the subspace constraints enforce size-consistency and a correct dissociation, but do not improve the accuracy of the method at short bond lengths, where they are not active. They only become active when one or more bonds are stretched. Furthermore, while only a small number of subspace constraints suffices to obtain the correct dissociation, the constraints are geometry dependent. They are therefore quite laborious to apply to large potential energy surfaces
2010-07-08T00:00:00Z