Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem (original) (raw)
Related papers
Exact ionization potentials from wavefunction asymptotics: The extended Koopmans' theorem, revisited
Chemical Physics, 2009
A simple explanation is given for the exactness of the extended Koopmans' theorem, (EKT) for computing the removal energy of any many-electron system to the lowest-energy ground state ion of a given symmetry. In particular, by removing the electron from a ``removal orbital'' of appropriate symmetry that is concentrated in the asymptotic region, one obtains the exact ionization potential and the exact Dyson orbital for the corresponding state of the ion. It is argued that the EKT is not restricted to many-electron systems but holds for any finite many-body system, provided that the interaction vanishes for increasing interparticle distance. A necessary and sufficient condition for the validity of the EKT for any state (not just the lowest-energy states of a given symmetry) in terms of the third-order reduced density matrix is stated and derived.
Critical thoughts on computing atom condensed Fukui functions
The Journal of Chemical Physics, 2007
Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks.
Nuclear fukui functions from nonintegral electron number calculations
International Journal of Quantum Chemistry, 2007
Numerical results for the nuclear Fukui function (NFF) based on a nonintegral number of electrons methodology (NIEM) are reported for a series of simple diatomic molecules. A comparison with those obtained from other methodologies is focused on the estimation of the error associated with a finite difference approximation for the evaluation of the NFF. The dependence of NFFs on the type and size of the basis set is also discussed. The NIEM values are in close agreement with those obtained from a finite difference approximation using ΔN = ±1 with large basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
Comparison among Four Different Ways to Condense the Fukui Function
The Journal of Physical Chemistry A, 2005
Four different ways to condense the Fukui function are compared. Three of them perform a numerical integration over different basins to define the condensed Fukui function, and the other one is the most traditional Fukui function using Mulliken population analysis. The basins are chosen to be the basins of the electron density (AIM), the basins of the electron localization function (ELF), and the basins of the Fukui function itself. The use of the last two basins is new and presented for the first time here. It is found that the last three methods yield results which are stable against a change in the basis set. The condensed Fukui function using the basins of the ELF is not able to give information on the reactivity of an acceptor molecule. In general, the condensed Fukui function using the basins of the density or the basins of the Fukui function describe the reactivity trends well. The latter is preferred, because it only contains information about the Fukui function itself and it gives the right information for donor as well as acceptor centers.
Physical Chemistry Chemical Physics, 2014
The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results.
Condensation of frontier molecular orbital Fukui functions
Journal of Physical Chemistry A, 2004
A comparison of the regional Fukui index evaluation within the frontier molecular orbital (FMO) Fukui functions is presented. The atoms-in-molecules (AIM) real space-based condensation scheme is compared against a basis set-based condensation scheme and the reliability of the produced reactivity trends is compared. The AIM condensation scheme turns out to give the best results. Furthermore, the AIM atom condensed Fukui indexes can be formally proven to be nonnegative.
Analysis of the equation-of-motion theory of electron affinities and ionization potentials
Chemical Physics, 1976
An analysis of the equation-of-motion (EOM) method for computing molecular electron affinities and ionization potentials is presented. The method is compared with the Dyson equation approach of Green func:ion theory. Particular emphasis is devoted to clarifying the similarities between these two theories when carried out to second and to third order. The Epstein-Nesbet hamiltonian and the notion of diagonal scatteringrenormaliition have been used to systematize this corn-"
An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory ͑SP-DFT͒. The resulting new nuclear Fukui function indices ⌽ N␣ and ⌽ S␣ are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H 2 O, H 2 CO, and some simple nitrenes ͑NX͒ and phosphinidenes ͑PX͒, with X = H, Li, F, Cl, OH, SH, NH 2 , and PH 2 . Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions.
Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory
The Journal of Chemical Physics, 2005
An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory ͑SP-DFT͒. The resulting new nuclear Fukui function indices ⌽ N␣ and ⌽ S␣ are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H 2 O, H 2 CO, and some simple nitrenes ͑NX͒ and phosphinidenes ͑PX͒, with X = H, Li, F, Cl, OH, SH, NH 2 , and PH 2 . Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions.
Journal of Computational Chemistry, 2002
In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.