Conceptual Density Functional Theory under Pressure: Part I. XP-PCM Method Applied to Atoms

High pressure chemistry offers the chemical community a range of possibilities to control chemical reactivity, develop new materials and fine-tune chemical properties. Despite the large changes that extreme pressure brings to the table, the field has mainly been restricted to the effects of volume changes and thermodynamics with less attention devoted to electronic effects at the molecular scale. This paper combines the conceptual DFT framework for analyzing chemical reactivity with the XP-PCM method for simulating pressures in the GPa range. Starting from the new derivatives of the energy with respect to external pressure, an electronic atomic volume and an atomic compressibility are found, comparable to their enthalpy analogues, respectively. The corresponding radii correlate well with major known sets of this quantity. The ionization potential and electron affinity are both found to decrease with pressure using two different methods. For the electronegativity and chemical hardness, a decreasing and increasing trend is obtained, respectively, and an electronic volume-based argument is proposed to rationalize the observed periodic trends. The cube of the softness is found to correlate well with the polarizability, both decreasing under pressure, while the interpretation of the electrophilicity becomes ambiguous at extreme pressures. Regarding the electron density, the radial distribution function shows a clear concentration of the electron density towards the inner region of the atom and periodic trends can be found in the density using the Carbó quantum similarity index and the Kullback–Leibler information deficiency. Overall, the extension of the CDFT framework with pressure yields clear periodic patterns.

Conceptual DFT has provided a framework in which to study chemical reactivity. Since high pressure is more and more a tool to control reactions and fine-tune chemical properties, this variable is introduced into the CDFT framework.

Understanding Chemical Selectivity through Well Selected Excited States

In this publication, we propose a new set of reactivity/selectivity descriptors, derived within a Rayleigh-Schrödinger perturbation theory framework, for chemical systems undergoing an electrostatic (point-charge) perturbation. From the electron density polarization at first order, qualitative insight on reactivity is retrieved, while more quantitative information (noteworthy selectivity) can be obtained from either the second-order energy response or the number of shifted electrons under perturbation. Noteworthily, only a small number of excitations contribute significantly to the overall responses to perturbation, suggesting chemical reactivity could be foreseen by a careful scrutiny of the electron density reorganization upon excitation.

Molecular dynamics simulations of the structure and the morphology of graphene/polymer nanocomposites

Molecular dynamics simulations are performed to scrutinize the structure and morphology of three polymer/graphene nanocomposites.

Addition of in situ reduced amidinato-methylaluminium chloride to acetylenes

Two ethylene-bridged methylaluminium amidinates and one aluminium amidinate containing three terminal trimethylstannyl-ethynyl groups interconnected by π-coordinated potassium ions were prepared in situ. The re-oxidation of the ethylene-bridged compound by iodine followed by further reduction using the same activation procedure demonstrated the versatility of the approach. The reactivity of an ethylene-bridged methylaluminum amidinate towards HCl was examined to demonstrate the building block concept. DFT calculations were performed to gain insight into the mechanism of the in situ activation of diphenylacetylene.

Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

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.

Revealing the thermodynamic driving force for ligand-based reductions in quinoids; conceptual rules for designing redox active and non-innocent ligands

Metal and ligand-based reductions have been modeled in octahedral ruthenium complexes revealing metal-ligand interactions as the profound driving force for the redox-active behaviour of orthoquinoid-type ligands. Through an extensive investigation of redox-active ligands we revealed the most critical factors that facilitate or suppress redox-activity of ligands in metal complexes, from which basic rules for designing non-innocent/redox-active ligands can be put forward. These rules also allow rational redox-leveling, i.e. the moderation of redox potentials of ligand-centred electron transfer processes, potentially leading to catalysts with low overpotential in multielectron activation processes.

A time dependent DFT study of the efficiency of polymers for organic photovoltaics at the interface with PCBM

In this work an intuitive (TD-DFT) approach was developed to explain the experimental efficiencies seen for organic photovoltaic devices.

On the applicability of local softness and hardness

Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.-Eur. J. 2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be "reinterpreted". In fact, the local softness and hardness contain the same "potential information" and they should be interpreted as the "local abundance" or "concentration" of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction.

Conceptual DFT: the chemical relevance of higher response functions

In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e.g. on the local and global polarizability. Its derivatives may govern the influence of charge on the polarizability, the R-analogues being the nuclear Fukui function and the quadratic and cubic force constants. Although some of the higher order derivatives may be difficult to evaluate a comparison with the energy expansion used in spectroscopy in terms of nuclear displacements, nuclear magnetic moments, electric and magnetic fields leads to the conjecture that, certainly cross terms may contain new, intricate information for understanding chemical reactivity.

Quantum similarity study of atoms: a bridge between hardness and similarity indices

A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev's table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3<or=Z<or=103, using the best single configuration electron density functions available. Different hardness kernels were used and the importance of the different contributions to the kernel was investigated. The atomic self-similarities constructed in this way show a fair correlation with experimental atomic polarizability.

Quantum similarity study of atomic density functions: Insights from information theory and the role of relativistic effects

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev's table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge.

Spin-Polarized Conceptual Density Functional Theory Study of the Regioselectivity in Ring Closures of Radicals

The regioselectivity of ring-forming radical reactions is investigated within the framework of the so-called spin-polarized conceptual density functional theory. Two different types of cyclizations were studied. First, a series of model reactions of alkyl- and acyl-substituted radicals were investigated. Next, attention was focused on the radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals (a three-step mechanism). In both of these reactions, the approaching radical (carbon or nitrogen centered) adds to a carbon-carbon double bond within the same molecule to form a radical ring compound. In this process, the number of electrons is changing from a local point of view (a charge transfer occurs from one part of the molecule to another one) at constant global spin number Ns (both the reactant and the product ring compound are in the doublet state). It is shown that the experimentally observed regioselectivities for these ring-closure steps can be predicted using the spin-polarized Fukui functions for radical attack, f0NN(r).

A Computational and Conceptual Density Functional Theory Study of the Properties of Re and Tc Tricarbonyl Complexes

A computational and conceptual density functional study has been performed on metal tricarbonyl complexes (MTC) of both Re(I) and Tc(I). The fully optimized complexes of fac-[Tc(OH(2))(CO(3))](+) and mer-[Tc(OH(2))(CO(3))](+) show geometries that compare favorably with the X-ray data. These structures were used as a starting point to investigate the relative stability of MTC complexes with various ligands containing combinations of N, O, and S as chelating atoms and to evaluate the stabilizing/destabilizing influence of these ligands. Both for Tc and for Re complexes the nitrogen content turns out to be decisive in the stability of the metaltricarbonyl complexes, the finer details being determined by the hardness sequence N > O > S. As the core of the complexes, [(M(CO)(3)(+)], is hard, the main ordering parameter is changed as compared to our previous studies on Tc(V) [3+1] complexes where the number of sulfur atoms was decisive in accordance with the much softer character of the MOCl core. All results are successfully interpreted in terms of the hard and soft acids and bases principle (HSAB) at the local level.

Philicity indices within the spin-polarized density-functional theory framework

The electrophilicity index is analyzed within the framework of spin-polarized density-functional theory. In this context, constrained philicities, omega(N) identical with (mu(N))(2)(2eta(NN)), are introduced in order to define the capability of a system to acquire or donate electrons in a process at constant spin number. The spin-philicity/spin-donicity indices, omega(S)(+/-) identical with (mu(S) (+/-))(2)(2eta(SS)), are examined and rationalized here as the philicity of a given system to change its spin-polarization state, as being defined through the spin potential mu(S) and spin hardness eta(SS) for a process at constant number of electrons. The local extension of these indices has been also outlined and numerical results have been discussed on the analysis of the electrophilic nature of some simple carbene systems both in the singlet and triplet states.

Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory

An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices PhiNalpha and PhiSalpha 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 H2O, H2CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH2, and PH2. 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.

Spin-Polarized Conceptual Density Functional Theory Study of the Regioselectivity in the [2+2] Photocycloaddition of Enones to Substituted Alkenes

A study of the regioselectivity of the photochemical [2+2] cycloaddition of triplet enones with a series of ground-state electron-rich and electron-poor alkenes using density functional theory (DFT)-based reactivity descriptors is presented. Using the concepts of local softness combined with a local hard and soft acids and bases principle and a softness matching approach, the regioselectivity of this reaction can only be explained in the case of the interaction of the triplet enones with electron-rich alkenes. In the next part, the regioselectivity was assessed within the framework of conceptual spin-polarized conceptual DFT, considering response functions of the system's external potential v, number of electrons N, and spin number NS (with NS being the difference between the number of alpha and beta electrons in the spin-polarized system). Within this theory, the concepts of local spin philicity and donicity are introduced. Using the spin philicity concept, the regioselectivity can almost be completely interpreted as resulting from the interaction of the site on the alkene with the highest spin philicity (i.e., lowest destabilization upon increasing spin number) with the site showing the highest change of spin number on the enone expected to result in the largest stabilization of this species.

Theoretical study revealing the functioning of a novel combination of catalytic motifs in histone deacetylase

Histone deacetylases (HDACs) have recently attracted considerable interest as targets in the treatment of cell proliferative diseases such as cancer. In the present work, the chemical properties of the active site of HDAC were theoretically investigated at a high computational level. Evidence was gathered for a novel catalytic mechanism, which differs from a previous proposal in the native protonation state of the His-Asp dyads, and in the deprotonation of water as a distinct step in the mechanism.

Relative Stability of Mixed [3 + 1] Tc and Re Complexes: a Computational and Conceptual DFT Study

A computational and conceptual density-functional study has been performed on various [3 + 1] complexes of both Re(V) and Tc(V). The fully optimized complexes chloro(3-thiapentane-1,5-dithiolato)oxorhenium(V) and chloro(3-thiapentane-1,5-dithiolato)oxotechnetium(V) show geometries that compare favorably with the X-ray data. These structures were used as a starting point to investigate the relative stability of Tc(V) and Re(V) complexes with various ligands containing combinations of N, O, and S as chelating atoms and to evaluate the stabilizing/destabilizing influence of these N, O, and S combinations. For both Tc and Re complexes, the S content (number and position of S atoms) together with the presence of an oxygen as the central chelating atom turns out to be decisive in the stability of the tridentate complexes, the latter factor being strongly destabilizing and the former stabilizing. The stabilization sequences for both Tc and Re are shown to be identical in the gas phase and in aqueous solutions treated in a polarizable continuum model. The Re(V) complexes are found to be more stable than their Tc(V) analogues. All of the results are successfully interpreted in terms of the hard and soft acids and bases principle, applied at the local level. For this purpose, a softness value for Tc is obtained by interpolating softness trends in neighboring elements of rows 5 and 6 in the periodic table.

Density functional theory as a tool for the structure determination of radiation-induced bioradicals

The use of density functional methods for the elucidation of the structure of radiation-induced bio-radicals by comparison of computed and experimental EPR properties is discussed. Three case studies, radiation induced radicals of the amino acid alanine, steroid hormones and beta-D-fructose, with increasing degree of uncertainty about the proposed radical structures, are investigated. Next to the analysis of the isotropic and anisotropic components of the hyperfine tensor, also the direction cosines of the principal axes of this tensor were investigated in greater detail in the case of the beta-D-fructose radicals. Since all radicals considered in this contribution are formed in a solid matrix, also the question as to how to incorporate the effect of the molecular environment is addressed. It is concluded that the methodology outlined represents a powerful tool to aid experimentalists in the assignment of the contributions of various radicals contributing to the observed EPR spectra.

On the importance of the “density per particle” (shape function) in the density functional theory

The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(r) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential micro of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined.

Hirshfeld partitioning of the electron density: atomic dipoles and their relation with functional group properties

Atomic dipole moments, derived within the Hirshfeld partitioning of the molecular electron density, have been studied for compounds of the type H-X and Cl-X, for a series of functional groups X frequently encountered in organic molecules. In the case of the H-X compounds, the component of the atomic dipole moment on H along the axis connecting H with the central atom in X is found to be linearly correlated with the electronegativity of X, the hardness of X playing no significant role. In the case of the Cl-X compounds, the situation is less clear. However, evidence seems to point to the conclusion that for these compounds, also the group hardness plays an important role.

Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density

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.

Nitrous oxide as a 1,3-dipole: a theoretical study of its cycloaddition mechanism

The 1,3-dipolar cycloadditions of nitrous oxide and substituted alkynes have been studied at the B3LYP/6-31G(d,p) level. The reaction is controlled by LUMO (dipole)--HOMO (dipolarofile) and involves aromatic transition structures. The shape of the potential energy surface and the regioselectivity are not affected by the polarity of the solvents, except in the case of N2O + HC triple bond CSiH3. Different reactivity criteria including FMO coefficients product C, local softness differences Delta, magnetic susceptibility anisotropy chi(anis), and nucleus-independent chemical shifts NICS were used to predict the regioselectivity in all studied cases; the C, Delta criteria turn out to give the best results among them. The aromaticity of the transition structure is not a factor in determining the regiochemistry of the cycloaddtition reactions.

Theoretical Study of [2 + 1] cycloaddition of CO and CS to acetylenes forming cyclopropenones and cyclopropenethiones

The [2 + 1] cycloadditions of carbon monoxide and carbon monothioxide CX (X = O, S) to acetylenes (R1C triple bond CR2 with R1 = H, OH and R2 = CH3, OH, NH2, C6H5) have been studied at the B3LYP/6-311G(d,p) level. It has been shown that the reaction proceeds in two steps forming first an intermediate having the properties of both a carbene and a zwitterion followed by a ring closure leading to cyclopropenones or cyclopropenethiones. The solvent effect does not play an important role in the course of the cycloaddition. The estimation of the first vertical excitation energies by CIS and TD-B3LYP methods shows that the reactions likely take place in the ground state rather than in an excited state. All the studied cyclopropenones and cyclopropenethiones are aromatic as shown by their NICS values and confirmed by calculated and experimental NMR chemical shifts. Different reactivity criteria including HOMO coefficient, local softness, hardness, polarizability, and NICS are used to predict the site selectivity in all studied cases, and the NICS criterion seems to yield the best results among them.