Four alternatives to solve Schrödinger equation

Quantum chemistry describes the hydrogen atom as one of the few systems that permits an exact solution of the Schrödinger equation. Students tend to consider that little can be learned from the hydrogen atom and forget that it can be used as a standard to test numerical procedures used to calculate properties of multielectronic systems. In this paper, four different numerical procedures are described in order to solve the Schrödinger equation for the hydrogen atom. The basic motivation is to identify new insights and methods that can be obtained from the application of powerful numerical techniques in a well-known system.15917

Investigação de energias de ionização e intensidades vibracionais (IV) utilizando o modelo potencial simples

Resumo: Foram determinados os tensores polares, a partir de dados experimentais do espectro infravermelho em fase gasosa, para as moléculas de aleno, dos fluoroclorometanos e do isocianeto de metila. Os resultados obtidos são similares aos disponíveis na literatura para aleno e fluoroclorometanos, exceto para o CF3Cl. Outra etapa constitiu na determinação dos parâmetros do modelo de Siegbahn, seu coeficiente angular e linear, através de dados de energias de ionização de camadas internas experimentais ou teóricas e derivadas médias do momento dipolar para os átomos de nitrogênio, oxigênio, flúor, cloro e bromo. A seguir, estes parâmetros foram interpretados com o auxílio de quantidades como número atômico e raio de valência, como definido por Pauling. Finalmente, foi proposto um método para obtenção de dipolos atômicos, coerentes com as derivadas médias do momento de dipolo, a partir de derivadas do momento de segunda ordem. Tal método revelou-se adequado para moléculas lineares. Em outras moléculas, os termos de fluxo de carga e de dipolo não permitem o cálculo de todos os possíveis dipolos. Esta afirmação é suportada pela análise das cargas, dipolos atômicos e fluxos obtidos com o formalismo de Bader, os quais mostraram-se aptos a descrever força de uma partícula carregada sobre moléculas.Abstract: The polar tensors for allene, the fluorochloromethanes and methyl isocyanide molecules have been determined from infrared gas phase experimental data. The results obtained are similar to those available in the literature for allene and the flurochloromethanes, except for CF3Cl. Another stage consisted in the determination of Siegbahn model parameters, from experimental or theoretical core ionization energy and mean dipole moment derivative data, for nitrogen, oxygen, fluorine, chlorine and bromine atoms. These parameters have been interpreted using atomic numbers and valency radii, as defined by Pauling. Finally, a method for atomic dipole determination from second moment derivatives, consistent with mean dipole moment derivatives, has been proposed. This method was showed to be applicable to linear molecules. The charge and dipole flux terms do not permit the calculation of all possible dipoles in other molecules. This affirmation is supported by the analysis of charges, atomic dipoles and fluxes obtained from Bader´s formalism, that permit description of the force of a charged particle over a molecule

Electrostatic potentials and polarization effects in proton-molecule interactions by means of multipoles from the quantum theory of atoms in molecules

Some atomic multipoles (charges, dipoles and quadrupoles) from the Quantum Theory of Atoms in Molecules (QTAIM) and CHELPG charges are used to investigate interactions between a proton and a molecule (F2, Cl2, BF, AlF, BeO, MgO, LiH, H2CO, NH3, PH3, BF3, and CO2). Calculations were done at the B3LYP/6-311G(3d,3p) level. The main aspect of this work is the investigation of polarization effects over electrostatic potentials and atomic multipoles along a medium to long range of interaction distances. Large electronic charge fluxes and polarization changes are induced by a proton mainly when this positive particle approaches the least electronegative atom of diatomic heteronuclear molecules. The search for simple equations to describe polarization on electrostatic potentials from QTAIM quantities resulted in linear relations with r-4 (r is the interaction distance) for many cases. Moreover, the contribution from atomic dipoles to these potentials is usually the most affected contribution by polarization what reinforces the need for these dipoles to a minimal description of purely electrostatic interactions. Finally, CHELPG charges provide a description of polarization effects on electrostatic potentials that is in disagreement with physical arguments for certain of these molecules. (c) 2012 Wiley Periodicals, Inc.CNPqCNPqFAPESPFAPES

The infrared fundamental intensities of some cyanopolyynes

Some cyanopolyynes, HCnN (n = 1, 3, ... , 17), are investigated by means of calculations at the MP2/cc-pVTZ and CCSD/cc-pVDZ levels. Although the MP2/cc-pVTZ results for geometries and molecular dipole moments are encouraging, the CCSD/cc-pVDZ level was superior for the study of infrared fundamental intensities. The main bands are also analyzed with a charge-charge flux-dipole flux (CCFDF) partition model based on quantities given by the Quantum Theory of Atoms in Molecules (QTAIM). The intensity of vibrations corresponding to the stretching of CH bonds (3471-3473 cm(-1)) increases in line with the number of carbon atoms (from 61 to 146 km mol(-1) between HCN and HC13N). This increase is due to the charge flux contribution while the other contributions remain roughly unaltered except for HCN. Moreover, the hydrogen atom loses an almost constant amount of electronic charge during the CH bond enlargement and a small fraction of this charge spreads to atoms farther and farther away from hydrogen as the molecule size increases. The band associated with the doubly degenerate CH bending vibrations (643-732 cm(-1)) presents approximately the same intensity in all the studied cyanopolyynes (from 67 to 76 km mol(-1)). The CCFDF/QTAIM contributions are also nearly the same for these bending modes in HC5N and larger systems. The intensity of the mode mostly identified as CN stretching (around 2378-2399 cm(-1) except for HCN) increases from HCN up to HC7N (from 0.3 to 83 km mol(-1)) and nearly stabilizes around 80-90 km mol(-1) for larger systems. The CCFDF/QTAIM contributions for this mode also change significantly up to HC7N and remain almost constant in larger systems. We also observed the appearing of a very relevant band between 2283 and 2342 cm(-1). This mode is mainly associated with the symmetric stretching of CC triple bonds near the molecule center and exhibits large charge fluxes while the other contributions are almost negligible in the largest cyanopolyynes. The two vibrational bands associated with the smallest frequencies are also studied and extrapolation equations are suggested to predict their positions in larger cyanopolyynes. (C) 2012 Elsevier B.V. All rights reserved.FAPESPFAPESPCNPqCNPqCAPESCape

The generator coordinate method in the unrestricted Hartree-Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree-Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree-Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin-up and spin-down electrons what is a result from spin polarization. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012CNPqCNPqFAPESPFAPESPCAPESCAPE

A Charge–Charge Flux–Dipole Flux Analysis of Simple Molecular Systems with Halogen Bonds

The presence of halogen bonds (R–X···B; R = substituent group, X = halogen, and B = Lewis base) provides quite amazing molecular systems for electronic structure investigations, presenting unique characteristics of fundamental relevance to supramolecular chemistry among other areas. Here, we use a double-hybrid approach from Density Functional Theory and triple-ζ basis sets augmented with diffuse functions (B2PLYP/def2-TZVPD) to deal with a large group of simple molecular systems containing halogen bonds (XBs), focusing on geometrical structures, binding energies, harmonic vibrational frequencies, and fundamental infrared intensities. Next, the electron densities and their variations on vibrations are carefully studied with the Quantum Theory of Atoms in Molecules (QTAIM) formalism and the charge–charge flux–dipole flux (CCFDF) model. We notice that the R–X stretching mode usually shows vibrational frequency decrements and infrared intensifications during the XB formation. Such features were also observed in hydrogen bonds, although the explanation for the band strengthening is different. Surprisingly, the most important contribution to these intensity increments due to complexation is now the interaction term between the charge flux and dipole flux (CF × DF). Thus, the use of atomic dipoles is mandatory to fully understand this phenomenon. In fact, the huge charge flux contributions to changes in dipole moment derivatives of R–X stretchings on halogen bonding are no longer accompanied by opposite variations of similar magnitudes in polarizations described by atomic dipole fluxes, which provided nearly unaltered values during the XB formation. Thus, the electronic charge flux direction change that takes place in complexes (from B to R) now reinforces dipole moment derivative terms from such atomic polarizations (mainly from the X atom). This intermolecular charge flux seems to be responsible for the unusual features noticed in the R–X stretching mode with the CCDDF/QTAIM model

The ground-state potential energy curve of the radium dimer from relativistic coupled cluster calculations

The potential energy curve for the ground-state of radium dimer (Ra<inf>2</inf>) is provided by means of atomic and molecular relativistic coupled cluster calculations. The short-range part of this curve is defined by an equilibrium bond length of 5.324 Å, a dissociation energy of 897 cm-1, and a harmonic vibrational frequency of 20.5 cm-1. The asymptotic behavior at large interatomic distances is characterized by the van der Waals coefficients C<inf>6</inf> = 5.090 × 103, C<inf>8</inf> = 6.978 × 105, and C<inf>10</inf> = 8.786 × 107 atomic units. The two regions are matched in an analytical potential to provide a convenient representation for use in further calculations, for instance, to model cold collisions between radium atoms. This might become relevant in future experiments on ultracold, optically trapped, radioactive radium atoms that are used to search for a permanent electric dipole moment

A theoretical study on the XeF(2) molecule

A relativistic four-component study was performed for the XeF(2) molecule by using the Dirac-Coulomb (DC) Hamiltonian and the relativistic adapted Gaussian basis sets (RAGBSs). The comparison of bond lengths obtained showed that relativistic effects on this property are small (increase of only 0.01 angstrom) while the contribution of electron correlation, obtained at CCSD(T) or CCSD-T levels, is more important (increase of 0.05 angstrom). Electron correlation is also dominant over relativistic effects for dissociation energies. Moreover, the correlation-relativity interaction is shown to be negligible for these properties. The electron affinity, the first ionization potential and the double ionization potential are obtained by means of the Fock-space coupled cluster (FSCC) method, resulting in DC-CCSD-T values of 0.3 eV, 12.5 eV and 32.3 eV, respectively. Vibrational frequencies and some anharmonicity constants were also calculated under the four-component formalism by means of standard perturbation equations. All these molecular properties are, in general, ill satisfactory agreement with available experimental results. Finally, a partition in terms of charge-charge flux-dipole flux (CCFDF) contributions derived by means of the quantum theory of atoms in molecules (QTAIM) in non-relativistic QCISD(FC)/3-21G* calculations was carried out for XeF(2) and KrF(2). This analysis showed that the most remarkable difference between both molecules lies on the charge flux contribution to the asymmetric stretching mode, which is negligible in KrF(2) but important in XeF(2). (c) 2008 Elsevier B.V. All rights reserved