Molecular fragment shape variation index for functional groups and the holographic properties of electron density

For a specific functional group, considered as a molecular fragment, the rest of the molecule produces a range of interactions which influence various properties of the functional group. Considering a family of molecules with the “same” functional group, the range of variations in properties determines the range of chemical reactivity of the functional group, and a similar conclusion is valid for more general molecular fragments. By the application of conventional as well as more advanced indices of fragment properties, including local electron density shape characterization, various shape variation indices can be introduced for fragments, and their relations to the holographic properties of electron densities can be examined.     

Generalized chirality and symmetry deficiency

Some of the elementary properties of molecular electron densities are studied from the perspectives of generalizations of symmetry, symmetry deficiency, and in particular, chirality. A simple, information‐theoretical proof of the Hohenberg–Kohn theorem is discussed, and the information contents of local and global molecular electron densities are compared using a formulation of quantum chemistry on a compact manifold. One result, the “holographic electron density theorem”, involving a compactification step combined with analytic continuation, gives a tool for comparing local and global symmetry properties. The compact manifold quantum chemistry approach leads to a precise statement on the role of local molecular regions in determining global properties of complete, boundaryless molecules, resulting in constraints on their symmetry, chirality, and other types of symmetry deficiencies. A special similarity measure, the SLT measure, is used for generalized density domain comparisons, suitable in general for the comparison of semilattices with a tree structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Shape analysis of macromolecular electron densities

Macromolecular shape analysis, an important aspect of the interpretation and prediction of biochemical behavior, pharmaceutical drug action, and the properties of advanced materials, is a task of a high level of complexity, where both global shape features and detailed, local shape features are relevant. The methods developed for the study of shapes of small molecules, in terms of molecular isodensity contours (MIDCOs), are not ideally suited for large molecular systems. In particular, the shape analysis of ab initio quality macromolecular electron densities, obtained by the MEDLA (molecular electron density lego assembler) method, requires a new approach. In this contribution, the adaptation of the earlier shape group approach to the electron densities of large molecules, and two new techniques, the shape globe folding map and the self-avoiding MIDCO methods, will be described.     

In-depth quantum chemical investigation of electro-optical and charge-transport properties of trans-3-(3,4-dimethoxyphenyl)-2-(4-nitrophenyl)prop-2-enenitrile

The structural, electro-optical and charge-transport properties of compound trans-3-(3,4-dimethoxyphenyl)-2-(4-nitrophenyl)prop-2-enenitrile (DMNPN) were studied using quantum chemical methods. The neutral, cation and anion molecular geometries were optimized in the ground state using density functional theory (DFT) at the restricted and unrestricted B3LYP/6-31G** level of theory. The excited state geometries were optimized by applying time-dependent DFT at the TD-B3LYP/6-31G** level of theory. The absorption and fluorescence wavelengths were calculated at the TD-CAM-B3LYP/6-31G** and TD-LC-BLYP/6-31G** levels of theory. The distribution pattern of the charge densities on the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) are discussed. Intramolecular charge transfer was observed from the dimethoxyphenyl to (nitrophenyl)prop-2-enenitrile moieties. The detailed charge-transport behavior of the DMNPN molecule is investigated based on its ionization potential, electron affinity, hole and electron reorganization energies, hole and electron-transfer integrals, and hole and electron intrinsic mobilities. The total/partial densities of states and structure–property relationship are discussed in detail. The higher computed hole intrinsic mobility than electron intrinsic mobility reveals that DMNPN is an efficient hole-transport material.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

Density functional theory treatment of electron correlation in the nuclear-electronic orbital approach

This paper presents the nuclear-electronic orbital density functional theory [NEO-DFT(ee)] method for including electron-electron correlation and nuclear quantum effects self-consistently in quantum chemical calculations. The NEO approach is designed to treat a relatively small number of nuclei quantum mechanically, while the remaining nuclei are treated classically. In the NEO-DFT(ee) approach, the correlated electron density is used to obtain the nuclear molecular orbitals, and the resulting nuclear density is used to obtain the correlated electron density during an iterative procedure that continues until convergence of both the nuclear and electronic densities. This approach includes feedback between the correlated electron density and the nuclear wavefunction. The application of this approach to bihalides and acetylene indicates that the nuclear quantum effects do not significantly impact the electron correlation energy, but the quantum nuclear energy is enhanced in the NEO-DFT(ee) B3LYP method. The excellent agreement of the NEO-DFT(ee)-optimized bihalide structures with the vibrationally averaged geometries from grid-based quantum dynamical methods provides validation for the NEO-DFT(ee) approach. Electron-proton correlation could be included by the development of an electron-nucleus correlation functional. Alternatively, explicit electron-proton correlation could be included directly into the NEO self-consistent-field framework with Gaussian-type geminal functions.     

Electronic structure of functionalized thia- and calix[4]arenes

The electronic structure of calix[4]arene phosphine oxides (CPO) and thiacalix[4]arene phosphine oxides (TCPO) is studied by X-ray photoelectron and emission spectroscopy and quantum chemical methods. The electron density distribution over atoms contained in CPO and TCPO is analyzed. The structure of higher occupied molecular orbitals (HOMO) is examined. It is shown that HOMOs of these compounds mainly consist of contributions of oxygen 2p atomic orbitals (AOs) of phosphoryl and hydroxyl moieties and also bridging sulfur 3p AOs, which indicates the bifunctionality of the considered extractant molecules. The mutual effect of the lower and upper rims of CPOs and TCPOs as well as the effect of their structures on the electron density distribution over calixarene molecules is investigated.     

A survey of some theoretical studies of negative ions

The quantum chemical methods employed by us to investigate the stabilities, charge densities, and bonding characteristics of atomic and molecular anions are briefly reviewed. The results of our work on chemically interesting species are surveyed, as are our initial results on the treatment of solvation effects in anionic systems. Finally, a simple-minded approach to the problem of finding shape resonances for electron–atom scattering processes is outlined.     

Molecular quantum similarity of enantiomers: substituted allenes

Molecular quantum similarity is evaluated for enantiomers in the case of molecules possessing a chiral axis, as an extension of previous studies on molecules with a single asymmetric carbon atom. As a case study, the enantiomers of substituted allenes are examined. Next to studying global similarity, using the already existing similarity indices defined by Carbó and Hodgkin-Richards, we evaluate local similarity using our earlier proposed local similarity index based on the Hirshfeld partitioning, to quantify the consequences of Mezey's holographic electron density theorem in chiral systems. Furthermore, the relation between the optical activity and the dissimilarity is studied.     

Molecular quantum similarity and chirality: enantiomers with two asymmetric centra

Molecular quantum similarity is evaluated for enantiomers possessing two asymmetric carbon atoms, namely halogen substituted ethanes. This study is an extension of previous work performed on molecules with a single asymmetric carbon atom and molecules possessing a chiral axis. Global similarity and its local counterpart based on the Hirshfeld partitioning are evaluated. By these means we quantify the dissimilarity of enantiomers and illustrate Mezey's holographic electron density theorem in chiral systems. Furthermore, the relation between the optical activity and the dissimilarity is studied. Special attention is drawn to the meso compounds, since these isomers enable us to examine local chirality in an achiral system.     

A General Procedure to Obtain Quantum Mechanical Charge and Bond Order Molecular Parameters

In an approach alternative to that of Mayer, a Hermitian operator is defined within the LCAO MO framework, which allows to obtain molecular charges and bond orders as expectation values of the first and second-order densities respectively. Such expectation values result to be nothing else than Mullikens atom and bond populations. Thus, Mulliken populations appear to be non arbitrary condensed electron density partitions, obtained according to quantum mechanical usual procedures for molecular one and two electron observables. The theoretical simplicity of the outlined procedure can be easily extended in order to obtain the expectation values for higher-order electronic chemical bonds.     

Quantum Chemical Spin Densities for Radical Cations of Photosynthetic Pigment Models

The spin densities of radical cations of magnesium porphyrin, magnesium chlorine and a truncated chlorophyll a model are calculated with density‐functional theory and multiconfigurational quantum chemical methods. The latter serve as a reference for approximate density‐functional theory which yields spin densities that may suffer from the self‐interaction error. We carried out complete active space self‐consistent field calculations with increasing active orbital spaces to systematically converge qualitatively correct spin densities. In particular, for the magnesium chlorine and chlorophyll a model radical cations, this is not easy to achieve because of the lower symmetry compared to magnesium porphyrin. Strategies had to be employed which allowed us to consider very large active orbital spaces. We explored restricted active space self‐consistent field and density‐matrix renormalization group calculations. Based on these reference data, we assessed the accuracy of different density‐functional approximations. We show that in particular, exchange–correlation model potentials with correct asymptotic behavior yield good spin densities, and we find, in agreement with previous studies on different classes of compounds, that hybrid functionals systematically increase spin‐polarization effects with increasing amounts of exact exchange. Our results provide a starting point for investigations of spin densities of more complex systems such as the hinge model for the primary electron donor in photosystem II.     

磷在P-ZSM-5沸石中存在的形态

用密度泛函理论和ONIOM (our own N-layer integrated molecular orbital molecular mechanics)方法研究磷改性的ZSM-5沸石中含磷基团的可能存在形态. 计算的反应焓和自由能数据表明P-ZSM-5沸石中以磷进入骨架和在骨架外的形成磷酸根离子对是合理的稳定结构. 而且, 计算结果表明离子对模型F和G更适合在室温下存在, 磷进入骨架的酸性结构C'在高温下更稳定, 而磷进入骨架的结构C对温度变化不敏感. 计算得到的²⁷Al, ³¹P, ²⁹Si化学位移、酸性的变化趋势和结构参数与相关实验数据吻合.     

A quantum-mechanical study of inductive and steric effects in isoalkanes

The method of “quantum mechanics of atoms in molecules” was used to find the parameters of functional groups in isopropylalkanes. The relation between such concepts of the classic theory of the structure of molecules as inductive and steric effects and electron density distribution was shown. Branching could cause deformation of the shape of an atom in a molecule accompanied by changes in volume and energy with charge conservation. The degree of damping of intramolecular steric and inductive effects was substantiated and described. An analysis of transferability of groups and the corresponding parameters was performed to obtain procedures for calculating properties by additive methods.     

Molecular model with quantum mechanical bonding information

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.     

Multiscale modeling of materials based on force and charge density fidelity

The approximate representation of a quantum solid as an equivalent composite semiclassical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a SiO(2) nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.     

A Uniqueness Theorem of Molecular Recognition

Phrased in terms of electron density deformations due to molecular interactions, an optimality condition, and the fundamental holographic properties of molecular electron densities, it is shown that molecular recognition is necessarily unique. A simple proof is given and the connections of this result with the Duality Principle of Molecular Recognition and related Selectivity Measures for molecular recognition are discussed.     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.