post-SCF Levels Research Articles

Interpretation of exchange and correlation using natural orbital CI expansions

In this work we propose definitions of exchange and correlation at post-SCF level within the framework of the natural orbital CI expansion of the wave function. First, following the assumption that the Coulomb correlation is introduced through the crossed products of Slater determinants, we define exchange and correlation densities having a simple mathematical and physical interpretation and whose associated holes satisfy a series of necessary constrains and normalization rules. Thus, in our scheme the exchange and correlation densities are associated with intra- and inter-configurational terms, respectively. In turn, two different terms contribute to the correlation density. One stems from the fluctuations experienced by the 1-electron density among different electron configurations. A second term corresponds to the inter-configurational part of the 2-electron density. Expressions for post-SCF exchange and correlation potentials and bond orders have been obtained and implemented for the case of two electrons.

Electron Density Based Partitioning Scheme of Interaction Energies.

In this paper, a new partitioning of the complex interaction energy is proposed. This new partitioning is based on the decomposition of the one-electron and exchange-correlation densities into unperturbed and deformation densities. Thus, the proposed energy fragmentation can be applied at the SCF level and post-SCF levels as long as the corresponding density matrices have been evaluated previously. It provides the typical description of the complex interaction as a summation of electrostatic, exchange-repulsion, and polarization terms. However, the new method allows splitting up the exchange-repulsion into exchange and Pauli-repulsion energies. A full theoretical description of the method is presented, and some examples of its application to small complexes are discussed. A comparison with results obtained using perturbation methods is also carried out, showing that the first order terms obtained from symmetry adapted perturbation theories are perfectly reproduced with the new method. A clear bridge between qualitative deformation density plots and quantitative measures of the interaction energy components can be established within the framework of this new partitioning scheme, giving rise to a graphical and very intuitive interpretation of the complex formation.

Nonadditive interactions in ns2 and spin-polarized ns metal atom trimers

The origins of nonadditivity in the following groups of metal trimers are examined: alkali earth metals of the IIA group (Be, Mg, and Ca), Zn as a transition metal analog of this group, spin-polarized alkali metals from IA group (Li, Na, K), and the spin-polarized Cu as its transition metal analog. The nonadditive interactions in these trimers are analyzed using the following hierarchy of approximations: the Heitler-London, self-consistent field (SCF), and correlated levels of theory. The exchange nonadditivity, which is included at the Heitler-London level, constitutes a bulk of nonadditive interactions in these systems in their equilibrium structures. The SCF treatment reveals some unphysical characteristics. At the post-SCF levels of theory the multireference character of the wave function increases from atom to dimer to trimer. The role of configurations involving excitations ns-np increases in this sequence and it is the genuine nonadditive effect. There is also a dramatic change in the characteristics of the excited states upon formation of clusters. We use the parameters of these excited states to predict which complexes are bound by the unusually strong nonadditive interactions and which are not.

Second-order Møller–Plesset perturbation theory for computing molecular-field splitting: application to the S2p 3/2 level in C 2H 2 n+1 SF 5, n=0, 1, and 2

High-resolution molecular X-ray photoelectron spectra of second-row atoms may reveal broadening or even splitting of the 2p 3/2 peak as compared to the 2p 1/2 component of the spectrum. This splitting reflects the lifted degeneracy of atomic 2p orbitals at sites of less than cubic symmetry and is referred to as molecular-field splitting (MFS). The prospect of using second-order Møller–Plesset theory (MP2) for ab initio calculation of the MFS for sulfur 2p 3/2 levels is examined. This method is subsequently applied to compute the MFS in ethynyl, ethenyl, and ethyl sulfur pentafluoride, resulting in values of 80, 116 and 121 meV, respectively. The initial-state contribution to the splitting is analyzed in terms of asymmetry in the electron density at sulfur, on the one hand, and in terms of the sulfur-ligand overlap density and electron density at the groups bonded to sulfur, on the other. At the Koopmans' theorem level of theory, the main source of splitting in the title compounds is found to be s–d hybridization of sulfur. At post-SCF levels of theory, core-valence electron correlation contributes substantially to the MFS, in proportion to the occupational asymmetry of the S3p shell. The realization that mixing of sulfur atomic orbitals of the same parity may add important contributions to the electric-field gradient at the core, resolves the observed diversity in the relative importance of core-valence electron correlation between different classes of sulfur compounds.

Molecular optical rotation: an evaluation of semiempirical models

Ab initio optical rotations have been obtained for allene, 1,3-dichloroallene, H 2O 2, and H 2S 2 as a function of dihedral angles, both at SCF and post-SCF levels. The results have been used to test (a) the concept that the molecular optical rotation can be written as a ∑ i M i sin θ i , where θ i is the dihedral angle of the ith X–A–A–X type segment and M i is a parameter associated with that segment; and (b) Kirkwood's polarizability model. The predicted ab initio optical rotation was found to depend strongly on the level of ab initio theory used, so highest levels of theory are required for accurate predictions. The optical rotation patterns obtained using high-level ab initio theory for H 2O 2, H 2S 2 and allene, as a function of dihedral angles, are found to be in line with Kirkwood's polarizability model predictions but not with the ∑ i M i sin θ i predictions.

A preliminary study of monomer geometry effects in theoretical calculations of the interaction energy for weak molecular complexes

An analysis is made of the repercussion that the consideration of the geometrical deformation of the monomers and the basis set superposition error, BSSE, can have on the theoretical calculation of the interaction energy of a hydrogen-bonded complex. The calculations, applied to the (HF) 2 system at the SCF and MP2 levels, were performed using several medium-sized basis sets. The conclusion is that, in order to achieve a good response, the complex's optimum geometry for each basis set has to be used, since otherwise one has to take into account the contribution to the energy coming from the geometrical relaxation experienced by the partner interacting systems. It is also seen that the BSSE must be corrected by eliminating the overestimate that appears in the counterpoise (CP) method of Boys and Bernardi (Mol. Phys., 19 (1970) 53) and that is located in the CP correction of the electronic exchange component of the interaction energy. The conclusion reached are valid at both the SCF and post-SCF levels.

Structure and stability of various (C2,H5,Ge)+ ions: an ab initio molecular orbital study

Various (C 2 ,H 5 ,Ge) + stable isomers have been identified on the corresponding SCF 3-21G * potential energy surface. Twelve distinct structures have been characterized, and their relative stability has been evaluated at the correlated MP2 and QCISD(T) post-SCF levels of theory, with double-ζ quality basis sets. Several analogies do exist with the previously described (C 3 ,H 5 ) + species, although significant differences can be pointed out

Structure and stability of H4NO4+ ions: an ab initio theoretical investigation

Ab initio quantum-mechanical calculations, at the SCF and post-SCF level of theory, have been performed on various H 4 NO 4 + ions. The hydration of the two isomers of protonated nitric acid, i.e., the NO 2 + (H 2 O) and ON(OH) 2 + isomers, has been investigated, and the formation of two sable ion-molecule complexes has been evidenced, whose geometrie have been optimized at the SCF 6-31G** level of theory

Theoretical investigation of the relative stabilities of singlet and triplet disulfides

Ab initio molecular orbital calculations have been performed on the singlet ( 1A) and triplet ( 3A u) states of hydrogen persulfide (HSSH) at the SCF and post-SCF levels using a double zeta basis set augmented with polarization functions. The relative energies for this system were computed by many-body perturbation theory (MBPT) and coupled-cluster (CC) methods, indicating that the singlet and triplet states are both lower in energy than the isolated HS fragments. Structural information for 1[HSSH] determined at the SCF and post-SCF levels are in good agreement with experiment. The triplet state is very weakly bound (<5 kcal/mol) and lies approximately 50 kcal/mol above the singlet state.

MP4 Interaction energies and basis set superposition errors for the (H 2) 2dimer

The energy of formation of the T-shaped (H 2) 2 dimer is calculated using different basis sets and Møller-Plesset perturbation theory up to fourth order. The roles of the second-, third- and fourth-order contributions as well as that of the different excitations at the fourth-order level were investigated. The results suggest that a correction for basis set superposition error should be included at both the SCF and post-SCF levels.