Beyond electronegativity and local hardness: Higher-order equalization criteria for determination of a ground-state electron density

Higher-order global softnesses, local softnesses, and softness kernels are defined along with their hardness inverses. The local hardness equalization principle recently derived by the authors is extended to arbitrary order. The resulting hierarchy of equalization principles indicates that the electronegativity/chemical potential, local hardness, and local hyperhardnesses all are constant when evaluated for the ground-state electron density. The new equalization principles can be used to test whether a trial electron density is an accurate approximation to the true ground-state density and to discover molecules with desired reactive properties, as encapsulated by their chemical reactivity indicators.     

On the redistribution of electrons for chemical reaction systems

A regional density-functional theory is formulated and applied to the study of ground-state electron redistributions during the course of a chemical reaction. If for a given increment of the reaction process, accumulation of electrons occurs in a certain region of space, then it is called the dynamic acceptor region, denoted by P. The complement is called the dynamic donor region, denoted by Q. The regional energy itself is determined as a unique functional of the electron density of the total system. The regional transfer potentials are defined in such a way that they add to give the total chemical potential, and their values along the reaction coordinate are found to be different between P and Q. The difference between the regional transfer potentials is shown to provide the driving force for electron transfer from Q to P. A characteristic coordinate for following electron transfer and an associated excitation potential are introduced. The excitation potential is a measure of regional virtual excitation due to regional interactions. The regional transfer potential gives the local character of electron transferability, while the excitation potential gives the global character. The theory encompasses the concepts of regional hardness and softness and sheds light on the HSAB principle.     

Atomic and Ionic Radii of Elements 1–96

Atomic and cationic radii have been calculated for the first 96 elements, together with selected anionic radii. The metric adopted is the average distance from the nucleus where the electron density falls to 0.001 electrons per bohr³, following earlier work by Boyd. Our radii are derived using relativistic all‐electron density functional theory calculations, close to the basis set limit. They offer a systematic quantitative measure of the sizes of non‐interacting atoms, commonly invoked in the rationalization of chemical bonding, structure, and different properties. Remarkably, the atomic radii as defined in this way correlate well with van der Waals radii derived from crystal structures. A rationalization for trends and exceptions in those correlations is provided.     

Correlation energies in the spin-density functional formalism

It has been shown recently that dynamical correlation effects can be adequately described by using an electron-gas expression for correlation between electrons of different spins. In this paper the method is applied to the calculation of excitation energies for the first- and second-row atoms and to the determination of ground-state properties for small polyatomic molecules, such as CH₂, CH₄, CH ₄ ⁺ , CH ₅ ⁺ . Additionally, deficiencies of the method for cases with few electrons and strongly varying electron density are investigated and an empirical correction to the electron-gas approximation is proposed. This correction is based on atomic data and gives an overall improvement for test molecules with two to four electrons.     

Kinetic Energy Density of the Two-Electron Hookean Atom in Terms of the Ground-State Electron Density

An explicit expression is derived for the kinetic energy density, including the correlation contribution, in terms of the ground-state electron density for the two-electron Hookean atom. This model atom has the merit that while the electrons are tied to an origin by springs, the Coulomb interaction energy between the two electrons is fully incorporated.     

Application of potential constants: Molecular chemical potential changes on formation of heteronuclear diatomic molecules—VI

The harmonic and anharmonic potential (force) constants of heteronuclear diatomic molecules, which are usually available from normal coordinate analyses, are applied to problems of determining the molecular chemical potential changes on formation of such molecules. The approach developed here is mainly based on density—functional theory, that is, the respective atomic energies in a molecule are expanded with the numbers of electrons and the nuclear potentials. These expansions are allowable because the ground-state energy for a system of N electrons and given nuclear potential ν(r) is a functional of N and ν(r). To test the reliability of the approach, we have calculated the molecular chemical potentials of alkali halides and other heteronuclear diatomic molecules, and their results have been compared favorably with the data obtained from Sanderson's Principle and the ab initio SCF calculation. We have also estimated apparent chemical hardnesses as well as integral terms including Fukui functions that provide good measures for electron transfers between atoms on molecule formation. Brief discussions on the molecular chemical potential changes are given.     

Water induced weakly bound electrons in DNA

We have studied the effect of humidity on the electronic properties of DNA base pairs. We found that the hydrogen links of the nucleobases with water molecules lead to a shift of the pi electron density from carbon atoms to nitrogen atoms and can change the symmetry of the wave function for some nucleobases. As a result, the orbital energies are shifted which leads to a decrease in the potential barrier for the hole transfer between the G-C and A-T pairs from 0.7 eV for the dehydrated case to 0.123 eV for the hydrated. More importantly, the pi electron density redistribution activated by hydration is enhanced by the intrastrand interactions. This leads to a modification of the nucleobase chemical structures from the covalent type to a resonance structure with separated charges, where some pi electrons are not locked up into the covalent bonds. Within the (G-C)(2) sequences, there is overlapping of the electronic clouds of such unlocked electrons belonging to the stacked guanines, that significantly increases the electron coupling between them to V(DA)=0.095 eV against the V(DA)=0.025 eV for the dehydrated case. Consequently, the charge transfer between two guanines within the (G-C)(2) sequences is increased by 250 times due to hydration. The presence of nonbonded electrons suppress the band gap up to approximately 3.0 eV, that allows us to consider DNA as a narrow band gap semiconductor.     

Clarification of the role of protein in carbonmonoxy myoglobin by investigating electronic states

This article reports the proton tautomerization effects of distal histidine residues in carbonmonoxy myoglobin according to the density functional calculations of the whole protein. The electron eigenstates and electrostatic potential (ESP) distributed around heme and its pocket vary significantly depending on the protonation positions of the distal histidine residues. To investigate the range over which the electronic structures are affected by the proton tautomerization, the quantum mechanics/molecular mechanics (QM/MM) method is applied to probe the QM size to reproduce the atomic partial charges and ESP around the active center. Consequently, we show that these properties converged for the 300 pm QM/MM system in this study. During the analysis, we also find that amino residues such as Phe43, Val68, and Phe138 interact strongly with heme through orbital mixing, indicating that the protein is a medium not only interacting with the reaction center, but also buffering on electrons. © 2013 Wiley Periodicals, Inc.     

New Regularities Discovered in Properties of Boranes with Different Number of Electrons and Degree of Their Localization. Dicarboranes

New regularities were established for the properties of dicarboranes and their anions depending on the number of electrons and electronegativities of substituents. The property changes are quantitatively related to the degree of localization of the electron density on chemical bonds, such localization being determined by the energetics of the molecule. The conclusions made are based on the results of quantum-chemical calculations using the structural thermodynamic model.     

Correlation strength and information entropy

The correlation present in the nondegenerate ground state of an interacting Fermi system is discussed in terms of reduced density matrices and their cumulant expansion. By generalizing a result obtained for the interacting uniform electron gas (correlation induced exchange-hole narrowing), possible measures of the correlation strength in terms of natural occupation numbers (the eigenvalues of the true one-particle density matrix) are introduced. These quantities-the v-order nonidempotency and the information entropy of the natural occupation numbers-result from the correlated many-body wave function and characterize the ground-state correlation in addition to the usual correlation energy. The uniform electron gas serves as a first illustrative example. © 1995 John Wiley & Sons, Inc.     

Charge separation in ground-state 1,2,4,5-tetra-substituted benzene derivatives

The conditions required for a formal biradical to exist in a zwitterionic form in the ground state are discussed following the recent experimental observation of zwitterionic structure in the ground state of a quinoid molecule (di-tert-butyl derivative of 2,5-diamino-1,4-benzoquinonediimine, I). A unique characteristic of molecules of this class is the fact that they may be considered as being formed by the union of two radicals, each having an odd number of pi electrons. In the case of I, one fragment carries the two amino group having 7 pi electrons; it acts as the electron donor. The other fragment carries the two oxygen atoms (carrying 5 pi electrons) and acts as an electron acceptor. A model that predicts the properties of these systems is presented, based on previous work on non-Kekule hydrocarbons(2,3) and on the electron donating and attracting properties of the donor and acceptor groups, respectively. The zwitterion is formed by an electron transfer leading to two subunits carrying 6 pi electrons each and may become more stable than the triplet biradical even in the gas phase (i.e., in the absence of an external field) if the ionization potential of the donor is small (of the order of 3-4 eV). In some cases solvation in a polar solvent is required to make the zwitterionic form the lowest energy species on the ground-state surface. The 'spacer' between the donor and acceptor groups (which need not be necessarily derived from an aromatic structure) can be varied and influences the overall dipole moment that is calculated in some cases to be quite large (over 20 D in the gas phase).     

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.     

Analogies and differences between two ways to evaluate the global hardness

The weight of the energetic components (electronic kinetic, electron-nucleus and electron-electron Coulombic, and correlation energies) of the ionization potential, electron affinity, chemical potential, and global hardness is evaluated and contrasted with the energetic components of the hardness kernel and the experimental values of these properties for 40 systems. The contrast of the hardness terms obtained from finite difference and hardness kernel gives some insight on the possible implications to differentiate the electronic energy with respect to the number electrons or the electron density.     

Hydrogen bonding and reactivity of water to azines in their S1 (n,π*) electronic excited states in the gas phase and in solution

A unified picture is presented of water interacting with pyridine, pyridazine, pyrimidine, and pyrazine on the S(1) manifold in both gas-phase dimers and in aqueous solution. As (n,π*) excitation to the S(1) state removes electrons from the ground-state hydrogen bond, this analysis provides fundamental understanding of excited-state hydrogen bonding. Traditional interpretations view the excitation as simply breaking hydrogen bonds to form dissociated molecular products, but reactive processes such as photohydrolysis and excited-state proton coupled electron transfer (PCET) are also possible. Here we review studies performed using equations-of-motion coupled-cluster theory (EOM-CCSD), multireference perturbation theory (CASPT2), time-dependent density-functional theory (TD-DFT), and excited-state Monte Carlo liquid simulations, adding new results from symmetry-adapted-cluster configuration interaction (SAC-CI) and TD-DFT calculations. Invariably, gas-phase molecular dimers are identified as stable local minima on the S(1) surface with energies less than those for dissociated molecular products. Lower-energy biradical PCET minima are also identified that could lead to ground-state recombination and hence molecular dissociation, dissociation into radicals or ions, or hydration reactions leading to ring cleavage. For pyridine.water, the calculated barriers to PCET are low, suggesting that this mechanism is responsible for fluorescence quenching of pyridine.water at low energies rather than accepted higher-energy Dewar-benzene based "channel three" process. Owing to (n,π*) excitation localization, much higher reaction barriers are predicted for the diazines, facilitating fluorescence in aqueous solution and predicting that the as yet unobserved fluorescence from pyridazine.water and pyrimidine.water should be observable. Liquid simulations based on the assumption that the solvent equilibrates on the fluorescence timescale quantitatively reproduce the observed spectral properties, with the degree of (n,π*) delocalization providing a critical controlling factor.     

Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation

Pairwise interaction correction (PIC) is introduced to account for electron density polarization due to short-range interactions such as hydrogen bonding and close contact between molecular fragments in the molecular fractionation with conjugated caps density matrix (MFCC-DM) approach for energy calculation of protein and other polymers [Chen et al., J. Chem. Phys. 122, 184105 (2005)]. With this PIC, the accuracy of the calculated protein energy and other electronic properties are improved, and the MFCC approach can be applied to study real proteins with short-range structural complexity. In the present MFCC-DM-PIC approach, the short-range interresidual interactions are represented by a pair of small molecules (interacting units) which are made from the two residues that fall within a certain distance criterion. The density matrices of fragments, concaps, interacting units and pairs are calculated by conventional Hartree-Fock or density functional theory methods and are combined to construct the full density matrix which is finally employed to calculate the total energy, electron density, electrostatic potential, dipole moment, etc., of the protein. Numerical tests on seven conformationally varied peptides are presented to demonstrate the accuracy of the MFCC-DM-PIC method.     

Surface chemistry: a non-negligible parameter in determining optical properties of small colloidal metal nanoparticles

Surface chemistry can become pronounced in determining the optical properties of colloidal metal nanoparticles as the nanoparticles become so small (diameters <20 nm) that the surface atoms, which can undergo chemical interactions with the environment, represent a significant fraction of the total number of atoms although this effect is often ignored. For instance, formation of chemical bonds between surface atoms of small metal nanoparticles and capping molecules that help stabilize the nanoparticles can reduce the density of conduction band electrons in the surface layer of metal atoms. This reduced electron density consequently influences the frequency-dependent dielectric constant of the metal atoms in the surface layer and, for sufficiently high surface to volume ratios, the overall surface plasmon resonance (SPR) absorption spectrum. The important role of surface chemistry is highlighted here by carefully analyzing the classical Mie theory and a multi-layer model is presented to produce more accurate predictions by considering the chemically reduced density of conduction band electrons in the outer shell of metal atoms in nanoparticles. Calculated absorption spectra of small Ag nanoparticles quantitatively agree with the experimental results for our monodispersed Ag nanoparticles synthesized via a well-defined chemical reduction process, revealing an exceptional size-dependence of absorption peak positions: the peaks first blue-shift followed by a turnover and a dramatic red-shift as the particle size decreases. A comprehensive understanding of the relationship between surface chemistry and optical properties is beneficial to exploit new applications of small colloidal metal nanoparticles, such as colorimetric sensing, electrochromic devices, and surface enhanced spectroscopies.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Optimized effective potentials yielding Hartree-Fock energies and densities

It is commonly believed that the exchange-only optimized effective potential (OEP) method must yield total energies that are above corresponding ground-state Hartree-Fock (HF) energies except for one- and two-electron systems. We present a simple procedure for constructing local (multiplicative) exchange potentials that reproduce exactly the HF energy and density in any finite basis set for any number of electrons. For any finite basis set, no matter how large, there exist infinitely many such OEPs, which questions their suitability for practical applications.