Roberto Flores-Moreno

Efficient and reliable numerical integration of exchange-correlation energies and potentials

An adaptive numerical integrator for the exchange-correlation energy and potential is presented. It uses the diagonal elements of the exchange-correlation potential matrix as a grid generating function. The only input parameter is the requested grid tolerance. In combination with a defined cell function the adaptive grid generation scales almost linear with the number of basis functions in a system. With the adaptive numerical integrator the self-consistent field energy error, which is due to the numerical integration of the exchange-correlation energy, converges with increasing adaptive grid size to a reference value. The performance of the adaptive numerical integration is analyzed using molecules with first, second, and third row elements. Especially for transition metal systems the adaptive numerical integrator shows considerably improved performance and reliability.

Influence of Endohedral Confinement on the Electronic Interaction between He atoms: A He2@C20H20 Case Study

The electronic interaction between confined pairs of He atoms in the C(20)H(20) dodecahedrane cage is analyzed. The He-He distance is only 1.265 A, a separation that is less than half the He-He distance in the free He dimer. The energy difference between the possible isomers is negligible (less than 0.15 kcal mol(-1)), illustrating that there is a nearly free precession movement of the He(2) fragment around its midpoint in the cage. We consider that a study of inclusion complexes, such as the case we have selected and other systems that involve artificially compressed molecular fragments, are useful reference points in testing and extending our understanding of the bonding capabilities of otherwise unreactive or unstable species. A key observation about bonding that emerges uniquely from endohedral (confinement) complexes is that a short internuclear separation does not necessarily imply the existence of a chemical bond.

Symmetry Conservation in Fukui Functions

The problem of symmetry breaking in the evaluation of Fukui functions is addressed. It is also demonstrated that a reliable solution of the problem can be achieved using analytic methods. An automatic method that avoids occurrence of symmetry breaks has been implemented in a computer code and is described here. Negative regions of the Fukui function are shown to play a key role for the interpretation of reactivity. Example plots are presented for diatomic molecules, inorganic molecules, conjugated systems, and molecular cages. The potentiality of the Fukui functions as molecular scalar fields for prediction and analysis of regioselectivity is enhanced. Its advantages with respect to the use of condensed Fukui functions are discussed.

Auxiliary density perturbation theory

A new approach, named auxiliary density perturbation theory, for the calculation of second energy derivatives is presented. It is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn-Sham equations the perturbed density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary density perturbation approach match quantitative with the ones from standard density functional theory if augmented auxiliary function sets are used. The computational advantages of auxiliary density perturbation theory are discussed, too.

Assessment of transition operator reference states in electron propagator calculations

The transition operator method combined with second-order, self-energy corrections to the electron propagator (TOEP2) may be used to calculate valence and core-electron binding energies. This method is tested on a set of molecules to assess its predictive quality. For valence ionization energies, well known methods that include third-order terms achieve somewhat higher accuracy, but only with much higher demands for memory and arithmetic operations. Therefore, we propose the use of the TOEP2 method for the calculation of valence electron binding energies in large molecules where third-order methods are infeasible. For core-electron binding energies, TOEP2 results exhibit superior accuracy and efficiency and are relatively insensitive to the fractional occupation numbers that are assigned to the transition orbital.

Efficient evaluation of analytic Fukui functions.

An efficient method for the analytic evaluation of Fukui functions is proposed. Working equations are derived and numerical results are used to validate the method on medium size set of molecules. In addition to the obvious advantages of analytic differentiation, the proposed method is efficient enough to be considered a practical alternative to the finite difference formulation used routinely. The reliability of the approximations used here is demonstrated and discussed. Problems found in other methods for prediction of electrophilic centers are corrected automatically when using the new method.

Time-dependent auxiliary density perturbation theory.

The recently developed auxiliary density perturbation theory is extended to time-dependent perturbations. As its static counterpart, it is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed through one auxiliary function density. As in the case of static perturbations a noniterative alternative to the corresponding coupled perturbed Kohn-Sham method is formulated. The new methodology is validated by local and gradient corrected dynamical polarizability calculations. Comparison with experiment indicates that for low frequencies reliable dynamical polarizabilities are obtained. Our discussion also shows that the computational performance of time-dependent auxiliary density perturbation theory is similar to the previously described static approach. In order to demonstrate the potential of this new methodology, dynamic polarizabilities of C(60), C(180), and C(240) are calculated.

Quasiparticle virtual orbitals in electron propagator calculations

The computational limits of accurate electron propagator methods for the calculation of electron binding energies of large molecules are usually determined by the rank of the virtual orbital space. Electron density difference matrices that correspond to these transition energies in the second-order quasiparticle approximation may be used to obtain a virtual orbital space of reduced rank that introduces only minor deviations with respect to the results produced with the full, original set of virtual orbitals. Numerical tests show the superior accuracy and efficiency of this approach compared to the usual practice of omission of virtual orbitals with the highest energies.

Half‐numerical evaluation of pseudopotential integrals

A half‐numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two‐dimensional angular and one‐dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l‐quantum number. The radial integrals are calculated by an adaptive one‐dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed.

A generalized any-particle propagator theory: prediction of proton affinities and acidity properties with the proton propagator.

We have recently extended the electron propagator theory to the treatment of any type of particle using an Any-Particle Molecular Orbital (APMO) wavefunction as reference state. This approach, called APMO/PT, has been implemented in the LOWDIN code to calculate correlated binding energies, for any type of particle in molecular systems. In this work, we present the application of the APMO/PT approach to study proton detachment processes. We employed this method to calculate proton binding energies and proton affinities for a set of inorganic and organic molecules. Our results reveal that the second-order proton propagator (APMO/PP2) quantitatively reproduces experimental trends with an average deviation of less than 0.41 eV. We also estimated proton affinities with an average deviation of 0.14 eV and the proton hydration free energy using APMO/PP2 with a resulting value of -270.2 kcal/mol, in agreement with other results reported in the literature. Results presented in this work suggest that the APMO/PP2 approach is a promising tool for studying proton acid/base properties.