Concepts, Methods and Applications of Quantum Systems in Chemistry and Physics

Chemical Semantics, Inc. (CSI) is a new start-up devoted to bringing the Semantic Web to chemistry and biochemistry. The semantic web is referred to as Web 3.0 or alternatively the Web of Data or the Web of Meaning. It does not replace the existing World Wide Web but augments it, placing data on the web in a structured form such that the data has “meaning” and computers can understand it. CSI has created a demonstration portal for exploring this new technology, specifically at this point for data created by quantum chemistry calculations. This paper describes the basics of a semantic web portal and the fundamental technology we have used in developing it.

We refer to atomic wave functions that contain the interelectron distances as “explicitly correlated”; we consider here situations in which an explicit correlation factor \(r_{ij}\) can occur as a power multiplying an orbital functional form (a Hylleraas function) and/or in an exponent (producing exponential correlation). Hylleraas functions in which each wave-function term contains at most one linear \(r_{ij}\) factor define a method known as Hylleraas-CI. This paper reviews the analytical methods available for evaluating matrix elements involving exponentially-correlated and Hylleraas wave functions; attention is then focused on computation of integrals needed for the kinetic energy. In contrast to orbital-product and exponentially-correlated wave functions, no general formulas have been developed by others to relate the kinetic-energy integrals in Hylleraas-CI (or its recent extension by the Nakatsuji group) to contiguous potential-energy matrix elements. The present paper provides these missing formulas, obtaining them by using relevant properties of vector spherical harmonics. Validity of the formulas is confirmed by comparisons with kinetic-energy integrals obtained in other ways.

To save time and computer resources, we made an attempt to design reasonable yet simple structural indicators to identify weak chemical bonds, instead of performing numerous, tedious calculations of individual bond dissociation energies (BDEs) for all bonds within a molecule. Based on the commonly available structure-property indicators for bond strength, such as bond length (R), the Mulliken interatomic electron number (MIEN), the Wiberg bond order (WBO), and BDE, we have created two new bond-strength indicators, i.e., M = MIEN/R and K = (WBO × MIEN)/R², which shall be directly used to efficiently identify almost all weak bonds with BDE below 350 kJ/mol. If several bonds of the same type attain the same smallest values of M or K, values of the electron density at the bond critical points (ρ _c ) alone can almost always pinpoint the weakest bond from the set of weak bonds, greatly reducing the amount of efforts in carrying out the calculations of the BDEs of the corresponding bonds.

We present the fundamentals of an advanced relativistic approach, based on the Gell-Mann and Low formalism, to studying spectroscopic characteristics of the multicharged ions in plasmas, in particular, computing the electron-ion collision strengths, cross-sections etc. The approach is combined with relativistic many-body perturbation theory with the Debye shielding model Hamiltonian for electron-nuclear and electron-electron systems. The optimized one-electron representation in the perturbation theory zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest perturbation theory corrections to the radiation widths of atomic levels. The computation results on the oscillator strengths and energy shifts due to the plasmas environment effect, the electron-collision strengths, collisional excitation and de-excitation rates for a number of the Be- and Ne-like ions of argon, nickel and krypton embedded to different types of plasmas environment (with temperature 0.02–2 keV and electron density 10¹⁶–10²⁴ cm⁻³) are presented and analyzed.

We present the fundamentals of a consistent relativistic theory of spectra of the exotic pionic atomic systems on the basis of the Klein-Gordon-Fock equation approach and relativistic many-body perturbation theory (electron subsystem). The key feature of the theory is simultaneous accounting for the electromagnetic and strong pion-nuclear interactions by means of using the generalized radiation and strong pion-nuclear optical potentials. The nuclear and radiative corrections are effectively taken into account. The modified Uehling-Serber approximation is used to take into account for the Lamb shift polarization part. In order to take into account the contribution of the Lamb shift self-energy part we have used the generalized non-perturbative procedure, which generalizes the Mohr procedure and radiation model potential method by Flambaum-Ginges. There are presented data of calculation of the energy and spectral parameters for pionic atoms of the ⁹³Nb, ¹⁷³Yb, ¹⁸¹Ta, ¹⁹⁷Au, with accounting for the radiation (vacuum polarization), nuclear (finite size of a nucleus) and the strong pion-nuclear interaction corrections. The measured values of the Berkley, CERN and Virginia laboratories and alternative data based on other versions of the Klein-Gordon-Fock theories with taking into account for a finite size of the nucleus in the model uniformly charged sphere and the standard Uehling-Serber radiation correction are listed too.

The integrated chirality density of H\(_2\)X\(_2\) molecules is studied in viewpoints of the internal torque for the electron spin. Since the chirality density is proportional to the zeta potential, which is the potential of the zeta force, one of the torque for the electron spin, the distribution of the chirality density affects the distribution of the internal torque in molecules. It is seen that the integrated chirality density is larger for the larger atomic number. It is found that the integrated chirality density of H\(_2\)Te\(_2\) has the same sign as the parity-violating energy, while those of H\(_2\)O\(_2\) and H\(_2\)S\(_2\) are opposite to the sign of the parity-violating energy, and the dependence of the integrated chirality density of H\(_2\)Se\(_2\) on dihedral angle is significantly different from that of the parity-violating energy.

The crystal structures of alkali metal borate salts are reviewed. A wide diversity of structures is noted. Structures with discrete ions containing two or more boron atoms are targeted for further study with ab initio methods (HF, B3LYP, and MP2) using modest basis sets (6-31G*, 6-31+G* and 6-311+G*). The ions identified for study are: [B₃O₆]³⁻, [B₃O₅(OH)₂]³⁻, [B₃O₄(OH)₄]³⁻, [B₃O₃(OH)₄]⁻, [B₄O₅(OH)₄]²⁻, [B₅O₆(OH)₄]⁻, [B₂O₅]⁴⁻, and [B₄O₉]⁶⁻. Some structurally related ions are examined, and an investigation of the diborates launched, including [B₂O(OH)₆]²⁻, observed in the magnesium salt, and [B₂(OH)₇]⁻, postulated as the intermediate responsible for signal exchange between borate anion and boric acid in ¹¹B NMR. The B-O bond distances and general structures are in good agreement with both crystallographic data and previous ab initio calculations.

The chemistry of boric acid and monomeric borates is reviewed. Following a discussion of the crystal structures and nuclear magnetic resonance studies, ab initio results are presented of molecular ortho- and metaboric acid, (tetrahydroxo)borate, and the hydrates of orthoboric acid and borate. The structures and vibrational frequencies are compared with experiment. Attempts to study their interconversion lead us to a discussion of oxodihydroxoborate (the conjugate base of boric acid), and of the hydroxide-boric acid complex. It is hypothesized that the conversion of boric acid into borate proceeds via the oxodihydroxoborate intermediate. Finally, the calculated structures of hydroxodioxo- and trioxoborate are compared with experiment.

We propose a simple construction method of the potential energy surface based on diabatic model for proton transfer in molecular pairs. Assuming two-state valence bond electronic wave functions as a diabatic basis, the diagonal and non-diagonal matrix elements in diabatic potential of water, ammonia, and imidazole pairs were obtained. The validity of the construction procedure was confirmed by comparing two adiabatic potentials: one was transformed from the obtained diabatic potential and another was calculated by DFT calculation. Diabatic potentials were also obtained using fewer reference points than conventional methods at various intermolecular distances. Finally, we discuss the resulting diabatic potential and non-diagonal elements in detail.

The possible stable geometries of the atmospheric negative core ion \( {\text{NO}}_{3}^{ - }\left({{\text{HNO}}_{3} } \right)_{2} \) and its monohydrate were theoretically investigated with the second order Møller-Plesset perturbation theory (MP2) in consideration of the effect of electron correlation. For both ionic clusters, we obtained the different stable geometries from the previous study by Drenck and coworkers (Int J Mass Spectrom 273:126–131, 2008) [1] with the density functional theory of Becke 3-parameters hybrid functional (B3LYP). The non-planar geometry with two hydrogen-bondings between one oxygen atom on \( {\text{NO}}_{3}^{ - } \) and each hydrogen atom of two HNO₃ fragments is found as the most stable structure of the core ion at 0 K. For the monohydrate, the most stable geometry at 0 K is found as the H ₂ O-embedded form in which one water molecule is located at the center of the cluster with hydrogen-bondings to \( {\text{NO}}_{3}^{ - } \) and HNO₃ fragments. Our results show that the hydrogen bond network of the core ion can be strongly perturbed by a single water molecule. We also discussed the relative abundance of conformers of these ionic clusters under a finite temperature.

In order to investigate chemical bonding between helium and hydrogen in the He–H model, coupled-cluster calculations were performed. In this study, three different hydrogen formal charges (positive, neutral and negative) were considered. In the case of positive hydrogen, it has been concluded that covalent bonding is formed between helium 1s orbital and hydrogen 1s orbital. Zero-point vibration energy was smaller than dissociation energy. It has been concluded that positive hydrogen is kept fixed at optimized structure.

Small neutral and ionic Rhodium clusters Rh_n (n = 6, 8, 13) are investigated by ab initio molecular orbital calculations with full optimization at the Restricted Open Shell Hartree-Fock (ROHF) level with a LANL2DZ basis set, and with the methods based on Density Functional Theory, B3LYP/MWB, B3LYP/PBE. The clusters are found favor close-packed icosahedron structures in contrast to previous theoretical predictions that rhodium clusters should favor cubic motifs. A range of spin multiplicities are investigated for each cluster and we present the minimum energy conformation along with the vertical and adiabatic ionization potentials.

We present the results of studying the radiation decay processes and computing the probabilities and oscillator strengths of radiative transitions in spectra of heavy Rydberg alkali-metal atoms. All calculations of the radiative decay (transitions) probabilities have been carried out within the generalized relativistic energy approach (which is based on the Gell-Mann and Low S-matrix formalism) and the relativistic many-body perturbation theory with using the optimized one-quasiparticle representation and an accurate accounting for the critically important exchange-correlation effects as the perturbation theory second and higher orders ones. The precise data on spectroscopic parameters (energies, reduced dipole transition matrix elements, amplitude transitions) of the radiative transitions nS_1/2→n′P_1/2,3/2 (n = 5, 6; n′ = 10–70), nP_1/2,3.2→n′D_3/2,5/2 (n = 5, 6; n′ = 10–80) in the Rydberg Rb, Cs spectra and the transitions 7S_1/2-nP_1/2,3/2, 7P_1/2,3.2-nD_3/2,5/2 (n = 20–80) in the Rydberg francium spectrum are presented. The obtained results are analyzed and discussed from viewpoint of the correct accounting for the relativistic and exchange-correlation effects. It has been shown that theoretical approach used provides an effective accounting of the multielectron exchange-correlation effects, including effect of essentially non-Coulomb grouping of Rydberg levels and others.

Annihilation momentum densities and vertex enhancement factors for positron annihilation on valence and core electrons of noble-gas atoms are calculated using many-body theory for s, p and d-wave positrons of momenta up to the positronium-formation threshold. The enhancement factors parametrize the effects of short-range electron-positron correlations which increase the annihilation probability beyond the independent-particle approximation. For all positron partial waves and electron subshells, the enhancement factors are found to be relatively insensitive to the positron momentum. The enhancement factors for the core electron orbitals are also almost independent of the positron angular momentum. The largest enhancement factor (\({\sim }10\)) is found for the 5p orbital in Xe, while the values for the core orbitals are typically \({\sim }1.5\).

Electronically non-adiabatic effects play an important role in many chemical reactions and light induced processes. Non-adiabatic effects are important, when there is an electronic degeneracy for certain nuclear geometries leading to a conical intersection between two adiabatic Born-Oppenheimer electronic states. The geometric phase effect arises from the sign change of the adiabatic electronic wave function as it encircles the conical intersection between two electronic states (e.g., a ground state and an excited electronic state). This sign change requires a corresponding sign change on the nuclear motion wave function to keep the overall wave function single-valued. Its effect on bimolecular chemical reaction dynamics remains a topic of active experimental and theoretical interrogations. However, most prior studies have focused on high collision energies where many angular momentum partial waves contribute and the effect vanishes under partial wave summation. Here, we examine the geometric phase effect in cold and ultracold collisions where a single partial wave, usually the s-wave, dominates. It is shown that unique properties of ultracold collisions, including isotropic scattering and an effective quantization of the scattering phase shift, lead to large geometric phase effects in state-to-state reaction rate coefficients. Illustrative results are presented for the hydrogen exchange reaction in the fundamental H+H\(_2\) system and its isotopic counterparts.

Arzanol (C₂₂H₂₆O₇) is a naturally occurring acylphloroglucinol present in Helichrysum italicum. It is the major responsible of its medicinal properties, which include anti-oxidant properties. In the arzanol molecule, the R of the COR group characterising acylphloroglucinols is a methyl group, and the two substituents in meta to COR are an α-pyrone ring, bonded to the benzene ring through a methylene bridge, and a prenyl chain. The high number of hydrogen bond donor and acceptor sites in the molecule entails an investigation taking into account solute-solvent hydrogen bonds in an explicit manner. The current work considers adducts of arzanol with explicit water molecules for a representative selection of its conformers. Adducts with one water molecule attached in turn to each of the H-bond donors or acceptors were calculated to estimate the strength with which each site can bind a water molecule. Adducts with varying numbers of water molecules were calculated to identify preferred arrangements of the water molecules around the various sites and around the molecule as a whole. These adducts also suggest possible geometries for the first solvation layer. All the adducts were calculated at the HF/6-31G(d, p) and the DFT/B3LYP/6-31+G(d, p) levels, with fully relaxed geometry.

Jozimine A₂ is a dioncophyllaceae-type naphthylisoquinoline alkaloid isolated from the root bark of an Ancistrocladus species from the Democratic Republic of Congo and exhibiting high antimalarial activity. It is the first naturally occurring dimeric naphthylisoquinoline of this type to be discovered. Its molecule consists of two identical 4′-O-demethyldioncophylline A units, with each unit containing an isoquinoline moiety and a naphthalene moiety. A thorough conformational study of this molecule was performed in vacuo and in three solvents with different polarities and different H-bonding abilities (chloroform, acetonitrile and water), using two levels of theory, HF/6-31G(d,p) and DFT/B3LYP/6-31+G(d,p). Intramolecular hydrogen bond (IHB) patterns were investigated considering all the possible options. Preferences for the mutual orientations of the moieties were identified through the potential energy profiles for the rotation of the single bonds between moieties. Harmonic vibrational frequencies were calculated to confirm the true-minima nature of stationary points, to obtain the zero point energies and to get indications about IHB strengths from red shifts. Intramolecular hydrogen bonds (O−H⋯O IHBs and O−H⋯π interaction) are the most stabilizing factors. The mutual orientations of the four moieties also have considerable influence and they prefer to be perpendicular to each other.

In previous papers, we revisited the Dirac equation and conjectured that the electron can be viewed as a massless charge spinning at light speed, this internal motion being responsible for the rest mass involved in external motions and interactions. Implications of this concept on basic properties such as time, space, electric charge, and magnetic moment were considered. The present paper investigates the deviations of the resulting gyromagnetic factor, fine-structure constant, and gravitational invariant from their integer approximates, and their implication in a better understanding of the electromagnetic, gravitational, and other interactions.

The scientific basis of Darwinian evolution is reconsidered from the recent progress in chemistry and physics. The idea, promoting a stochastic communication hypothesis, reflects Kant’s famed insight that ‘space and time are the two essential forms of human sensibility’, translated to modern practices of quantum science. The formulation is commensurate with pioneering quantum mechanics, yet extended to take account of dissipative dynamics of open systems incorporating some fundamental features of special and general relativity. In particular we apply the idea to a class of Correlated Dissipative Structures, CDS, in biology, construed to sanction fundamental processes in biological systems at finite temperatures, ordering precise space-time scales of free energy configurations subject to the Correlated Dissipative Ensemble, CDE. The modern scientific approach is appraised and extended incorporating both the material- as well as the immaterial parts of the Universe with significant inferences regarding processes governed by an evolved program. The latter suggests a new understanding of the controversy of molecular versus evolutionary biology. It is demonstrated by numerous examples that such an all-inclusive description of Nature, including the law of self-reference, widens the notion of evolution from the micro to the cosmic rank of our Universe.