Is there a quantum definition of a molecule?

The paper surveys how chemistry has developed over the past two centuries starting from Lavoisier’s classification of the chemical elements at the end of the eighteenth century; the subsequent development of the atomic–molecular model of matter preoccupied chemists throughout the nineteenth century, while the results of the application of quantum theory to the molecular model has been the story of this century. Whereas physical chemistry originated in the nineteenth century with the measurement of the physical properties of groups of chemical compounds that chemists identified as families, the goal of chemical physics is the explanation of the facts of chemistry in terms of the principles and theories of physics. Chemical physics as such was only possible after the discovery of the quantum theory in the 1920’s. By then the first of the sub‐atomic particles had been discovered and seemingly it is no longer possible to discuss chemical facts purely in terms of atoms and molecules – one has to recognize the electron and the nucleus, the parts of atoms. The combination of classical molecular structure with the quantum properties of the electron has given us a tremendously successful account of chemistry called ‘quantum chemistry’. Yet from the perspective of the quantum theory the deepest part of chemistry, the existence of chemical isomers and the very idea of molecular structure that rationalizes it, remains a central problem for chemical physics. This revised version was published online in July 2006 with corrections to the Cover Date.     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

α-Al2O3(0001)表面弛豫及其对表面电子态的影响

The relaxation and electronic structure of the α-Al2O3 (0001) super-cell (2×2) surface with single Al atoms layer-terminated are studied using ab initio quantum-mechanical calculations based on the density functional theory and pseudo potential method. The calculations employ slab geometry and periodic boundary conditions, with the occupied orbitals expanded in plane waves. It is found that the surface relaxation results in the change of surface electronic states by investigating the relaxation and the population of the Al-O atoms of the surface. By analyzing the difference of the density of state and electron charge density between the unrelaxed and relaxed surface, it is obvious that the α-Al2O3 (0001) crystal surface appears on the O-surface state from which is most contribution to the O2p states, and the surface electronic density plotted by electron localization function (ELF) shows the characteristics of surface bonding atoms. The ELF indicates the outmost Al-O ionic bonds of the relaxed surface are much stronger than that of the unrelaxed surface.     

Structure of X-ray photoelectron, emission, and conversion spectra and molecular orbitals of uranium compounds

The fine structure of X-ray photoelectron spectra of uranium compounds in the range of electron binding energies from 0 to ∼50 eV is largely determined by the electrons of the outer and inner valence molecular orbitals arising from the valence atomic shells, including the U6p and Lns low-energy occupied atomic shells. This result is in agreement with the data of the electronic structure calculations of these compounds and confirmed by the nuclear electron (conversion) and X-ray emission spectroscopic investigations. It is shown that the fine structure of X-ray photoelectron spectra associated with the electrons of inner valence molecular orbitals makes it possible to judge the participation of the electrons of the occupied atomic shells in chemical bonding, the structure of the nearest environments of the atom, and the bond lengths in the compounds. The overall contribution of the electrons of these molecular orbitals to the absolute value of binding energy may prove to be comparable to the contribution of the electrons of the outer valence molecular orbitals to atomic bonding. This is a new and important fact in chemistry. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 1037–1046, November–December, 1998.     

Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.     

Interesting periodic variations in physical and chemical properties of homonuclear diatomic molecules

We carry out a systematic study of various ground state and response properties of homonuclear diatomic molecules (from hydrogen to rubidium, including transition metals) as a function of atomic number of constituent atoms. We perform the ground state and response property calculations by using state of the art density functional theory/time dependent density functional theory. We observe that several properties of homonuclear diatomic molecules show periodic variations along rows and columns of the periodic table. The periodic variations in the ground state properties of diatomic molecules may be explained by the nature and type of the bond that exists between the constituent atoms. Similarly, the periodic variations in the response properties such as static dipole polarizability and strength of the van der Waals interaction between diatomic molecules have been correlated with the variations in metallic/nonmetallic character of the elements along the periodic table. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Use of Electron-Density Plots in Applied Quantum Chemistry

The uses in applied quantum chemistry of computer-produced three-dimensional diagrams of electron-density distributions are discussed. The two major catagories of such diagrams are contrasted; and advantages are described for plots showing as the third dimension the point-by-point electron density in a cross-sectional cut (corresponding to the other two dimensions) through a molecule. Examples are presented to show how these plots may be used (1) to assess the adequacies of a given mathematical representation employed in the calculation of a wavefunction, (2) to clarify the interrelationship between an individual molecular orbital and the atomic orbitals of the constituent atoms, as well as (3) to explain the canonical set of molecular orbitals of any selected molecule. Furthermore these plots serve(4) to demonstrate clearly a replication of key characteristics between certain molecular orbitals in different molecules. These examples are accompanied by others which indicate how the electron-density plots may be used(5) to understand and clarify accepted chemical dogma. Finally, the possibility is discussed of employing quantum calculations on a wider scale so as to be of value in the more practical aspects of chemistry.     

Construction of basis sets of hybrid atomic orbitals for describing the nonequivalent bonds of an atom with three neighboring atoms (sp 2 andsp 3 hybridization)

The paper describes methods for obtaining basis sets of sp² and sp³ hybrid atomic orbitals to describe nonequivalent chemical bonds in organic molecules with heteroatoms. Being affine, these basis sets present an alternative to the conventional basis sets of Cartesian atomic orbitals. Unlike the latter, the hybrid atomic orbitals are invariant to spatial rotations of molecules, thus providing the rotational invariance of the results of any semiempirical quantum chemical calculations. The construction of the basis sets of hybrid functions for atoms surrounded with three neighboring atoms (planar and nonplanar configurations) is considered in detail. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36. No. 6, pp. 963–968, November–December, 1995. Translated by I. Izvekova     

Quantum Monte Carlo Calculation of Correlation Effects on Bond Orders

We present a computational approach, using quantum Monte Carlo, that provides some insight into the effect of electron correlation on chemical bonding between individual pairs of atoms. Our approach rests upon a recently suggested relation between the bond order and charge fluctuations with respect to atomic domains. Within the present implementation we have taken a compromise between conceptual rigour and computational simplicity. In a first step atomic domains were obtained from Hartree-Fock (HF) densities, using Bader’s definition of atoms in molecules. These domains were used in a second step in quantum Monte Carlo calculations to determine bond orders for pairs of atoms. Correlation effects have been studied by comparison of HF bond orders with those obtained from pure diffusion quantum Monte Carlo calculations. We illustrate this concept for C–O and C–S bonds in different molecular environments. Our results suggest an approximate linear relation between bond order and bond length for these kinds of bonds.     

Superatomic chemistry

Superatoms are atomic clusters with tailored size and composition that mimic the chemistry of atoms in the periodic table. However, unlike the atoms whose chemistry is governed by their valence electron orbitals, the chemistry of superatoms is governed by their highest occupied molecular orbitals. In addition, due to their large size and non-spherical geometry, superatoms can promote unusual reactions and serve as the building blocks of cluster assembled materials with properties very different from conventional materials. This perspective highlights the unique role of superatoms in chemical and material sciences by focusing on superhalogens, which not only possess electron affinities larger than those of halogens but also can be stable when multiply charged. We discuss how these unique features of superhalogens enable noble gas atoms like argon to form chemical bonds at room temperature and zinc to exhibit an oxidation state of +3. The advantages of using superhalogens in the synthesis of water-resistant materials for solar cells, halogen-free electrolytes for solid-state batteries, and multiferroic materials are also discussed.     

Intermolecular charge transfer and hydrogen bonding in solid furan

The calculated structures of furan as a monomer, a dimer that was isolated from the crystal structure, and the full crystal structure have been thoroughly investigated by a combination of density functional theory (DFT) calculations and inelastic neutron scattering (INS) measurements. To improve our understanding of the nature and magnitude of the intermolecular interactions in the solid, the atoms in molecules (AIM) theory has been applied to the dimer and a cluster of eight monomers. After a careful topological study of the theoretical charge density and of its Laplacian, we have established the existence of C-H...pi, C-H...O, and H...H interactions between adjacent molecules in solid furan. The electron distribution has also been analyzed by performing natural bond orbital (NBO) calculations for the monomer and a H-bonded dimer. When the hydrogen bond is established between two adjacent furan rings, some electron charge is transferred from the pi electronic system of one furan ring to the other molecule in the dimer. This result provides a model of the interaction between end groups of neighboring chains of polyfuran and could be applicable to other conjugated polymers where the pi system is responsible for their conducting properties. To determine how the intermolecular bonds in the solid affect the vibrational dynamics in the periodic system, INS data were analyzed by performing molecular and periodic density functional calculations. Reasonable agreement is achieved, although we note that the poorest agreement is for modes involving hydrogen atoms.     

An ab initio evaluation of the role of p,π interaction: I. Ethylene derivatives

The RHF/6-311G(d) and MP2/6-311G(d) calculations with full geometry optimization were performed for XCH=CH₂ molecules (X = F, Cl, Br, CH₃, CH₂CH₃, CH₂F, CHO). The p _y electron density distribution in these molecules and the bonding molecular orbitals formed by the p _y orbitals of atoms of the planar fragment of these molecule (atomic orbitals whose symmetry axes are perpendicular to this plane) are not determined by the p,π conjugation between the lone electron pair of the heteroatom in substituent X and π electrons of the C=C bond. Changes in the population of the p _y orbitals of the halogen and carbon atoms in going from X = F to X = Cl and Br are not associated with changes in the extent of this p,π interaction. Taking into account the electon correlation in the MP2 method does not noticeably alter the features of the electron density distribution in these molecules estimated by restricted Hartree-Fock calculations.     

On the non-existence of parallel universes in chemistry

This treatise presents thoughts on the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or ‘bent’ to suit preconceived ideas. The former approach is embodied in the quantum theory of atoms in molecules (QTAIM), a theory based upon the properties of a system’s observable distribution of charge. Science is experimental observation followed by appeal to theory that, upon occasion, leads to new experiments. This is the path that led to the development of the molecular structure hypothesis—that a molecule is a collection atoms with characteristic properties linked by a network of bonds that impart a structure—a concept forged in the crucible of nineteenth century experimental chemistry. One hundred and fifty years of experimental chemistry underlie the realization that the properties of some total system are the sum of its atomic contributions. The concept of a functional group, consisting of a single atom or a linked set of atoms, with characteristic additive properties forms the cornerstone of chemical thinking of both molecules and crystals and Dalton’s atomic hypothesis has emerged as the operational theory of chemistry. We recognize the presence of a functional group in a given system and predict its effect upon the static, reactive and spectroscopic properties of the system in terms of the characteristic properties assigned to that group. QTAM gives physical substance to the concept of a functional group.     

Recommended Questions on the Road towards a Scientific Explanation of the Periodic System of Chemical Elements with the Help of the Concepts of Quantum Physics

Periodic tables (PTs) are the ‘ultimate paper tools’ of general and inorganic chemistry. There are three fields of open questions concerning the relation between PTs and physics: (i) the relation between the chemical facts and the concept of a periodic system (PS) of chemical elements (CEs) as represented by PTs; (ii) the internal structure of the PS; (iii)␣The relation between the PS and atomistic quantum chemistry. The main open questions refer to (i). The fuzziness of the concepts of chemical properties and of chemical similarities of the CE and their compounds guarantees the autonomy of chemistry. We distinguish between CEs, Elemental Stuffs and Elemental Atoms. We comment on the basic properties of the basic elements. Concerning (ii), two sharp physical numbers (nuclear charge and number of valence electrons) and two coarse fuzzy ranges (ranges of energies and of spatial extensions of the atomic orbitals, AOs) characterize the atoms of the CEs and determine the two-dimensional structure of the PS. Concerning (iii), some relevant ‘facts’ about and from quantum chemistry are reviewed and compared with common ‘textbook facts’. What counts in chemistry is the whole set of nondiffuse orbitals in low-energy average configurations of chemically bonded atoms. Decisive for the periodicity are the energy gaps between the core and valence shells. Diffuse Rydberg orbitals and minute spin–orbit splittings are important in spectroscopy and for philosophers, but less so in chemical science and for the PS.     

The bonding in the ozone molecule: From a different perspective

A new qualitative treatment of the bonding in ozone is presented. It is based upon a combination of several simple concepts: the nonparticipation of the pairs of electrons tightly held in the atomic 2s orbitals; simple overlap of the 2p orbitals to form sigma bonds; interaction of three 2p orbitals to yield bonding and nonbonding pi molecular orbitals that are populated by electron pairs; and van der Waals repulsion between the two terminal oxygen atoms forcing these atoms apart to yield the bond angle of 117° as a compromise. Both the assumptions and the resulting bonding picture are in accord with the photoelectron spectroscopic data, the results from sophisticated molecular orbital calculations, and the common physical properties of ozone.     

The First Subatomic Explanations of the Periodic System

Attempts to explain the periodic system as a manifestation of regularities in the structure of the atoms of the elements are as old as the system itself. The paper analyses some of the most important of these attempts, in particular such works that are historically connected with the recognition of the electron as a fundamental building block of all matter. The history of the periodic system, the discovery of the electron, and ideas of early atomic structure are closely interwoven and transcend the physics–chemistry boundary. It is pointed out that J. J. Thomson's discovery of the electron in 1897 included a first version of his electron atomic model and that it was used to suggest how the periodic system could be understood microphysically. Thomson's theory did not hold what it promised, but elements of it were included in Niels Bohr's first atomic model. In both cases, Thomson's and Bohr's, the periodic system played an important role, heuristically as well as justificatory. This revised version was published online in July 2006 with corrections to the Cover Date.     

Hydrophobic hydration

The problem of interaction between organic and water moieties (neutral or ionized water molecular species) is of particular interest in chemistry in view of its implications to physico-chemical behavior of chemical and biological systems. Hydration patterns which result from interaction between hydrophilic and hydrophobic species are non trivial in chemistry. The key issue is that water molecules are able to aggregate in extremely large variety of structural modes. Tetrahedral geometry of intermolecular bonding around water molecule is analogous in geometrical terms to that of intramolecular geometry of carbon atom, known as a source of infinite number of organic structures. In general, space filling with hydrogen bonded water molecules is rather low. It may be illustrated in the following way: volume of neonium atoms is comparable to that of water molecules whilst having atomic mass just 10% higher than molecular mass of water. Thus, liquid neonium and liquid water would have similar densities if molecular packing is of comparable efficiency. The real values are much different, however. Liquid neonium at its boiling temperature has density of 1.20 g cm^–3 , thus displaying significantly denser packing that that of water molecules. It certainly means that solid or liquid water has a ‘porous’ structure and may lead to molecular inclusion of foreign (guest) species in the intermolecular space of water framework. This property is not that simple, however, since inclusion of foreign (guest) species is, as a rule, associated with rearrangement of the host framework structure [1]. Anyway, inefficient packing of the mono-component host solid phases may be considered as a prerequisite for its pronounced clathration ability.     

Orbital views of molecular conductance perturbed by anchor units

Site-specific electron transport phenomena through benzene and benzenedithiol derivatives are discussed on the basis of a qualitative Hu?ckel molecular orbital analysis for better understanding of the effect of anchoring sulfur atoms. A recent work for the orbital control of electron transport through aromatic hydrocarbons provided an important concept for the design of high-conductance connections of a molecule with anchoring atoms. In this work the origin of the frontier orbitals of benzenedithiol derivatives, the effect of the sulfur atoms on the orbitals and on the electron transport properties, and the applicability of the theoretical concept on aromatic hydrocarbons with the anchoring units are studied. The results demonstrate that the orbital view predictions are applicable to molecules perturbed by the anchoring units. The electron transport properties of benzene are found to be qualitatively consistent with those of benzenedithiol with respect to the site dependence. To verify the result of the Hu?ckel molecular orbital calculations, fragment molecular orbital analyses with the extended Hu?ckel molecular orbital theory and electron transport calculations with density functional theory are performed. Calculated results are in good agreement with the orbital interaction analysis. The phase, amplitude, and spatial distribution of the frontier orbitals play an essential role in the design of the electron transport properties through aromatic hydrocarbons.