Pauli repulsions exist only in the eye of the beholder

This paper presents a rebuttal to the preceding paper in this issue entitled "Hydrogen-Hydrogen Bonding in Planar Biphenyl, Predicted by Atoms-In-Molecules Theory, Does Not Exist". The arguments presented therein are based on an arbitrary partitioning of the energy into contributions from physically unrealizable states of the system. The response given here is presented in terms of the Feynman, Ehrenfest, and virial theorems of quantum mechanics and the observable properties of a system. A reader is thus free to choose between subjectivity or physics.     

Comments on the status of the chemical bond in methods of quantum chemistry

Chemists do not take the view that chemistry can be derived from quantum mechanics by computations too literally; the difficulties are illustrated by the double bond concept. Quantum mechanics is very useful, but recent calculations have been mainly concerned with physical properties rather than chemical processes. In general, the chemical formula plays a central role in all interpretation of quantum-chemical results, thus suggesting that the chemical bond is a preexistent notion. Moreover, the Born–Oppenheimer approximation seems to be necessary for deriving the existence of bonds between atoms previously assigned to suitable positions. Recent analyses by Claverie and Diner, Woolley, Primas, and others are briefly recalled, concluding with an expression of hope that use of more general Hamiltonians can lead to progress in obtaining a fully independent quantum theory of chemistry.     

Interpreting geometric preferences in π‐stacking interactions through molecular orbital analysis

The preference of π‐stacking interactions for parallel‐displaced (PD) and twisted (TW) conformations over the fully eclipsed sandwich (S) in small π‐stacked dimers of benzene, pyridine, pyrimidine, 1,3,5‐trifluorobenzene, and hexafluorobenzene are examined in terms of enhancement of the inter‐ring density through mixing of the monomer orbitals (MOs). PD and/or TW conformations are consistent with a non‐zero “stack bond order” (SBO), defined in analogy to the bond order of conventional MO theory, as the difference in the occupation of bonding and antibonding π‐type dimer MOs. In the S conformation, the equal number of bonding and antibonding MOs cancel overall stack bonding character between the monomers for an SBO of zero and an overall repulsive interaction. PD from the S shifts the character of at least one antibonding combination of monomer π‐type MOs with nodes perpendicular to the coordinate for PD to bonding, leading to an attractive nonzero SBO. The inter‐ring density measured through the Wiberg bond index analysis shows an enhancement at the PD conformations consistent with greater interpenetration of the monomer densities. This intuitive bonding model for π‐stacking interactions is complementary to highly accurate calculations of π‐stacking energies and allows a predictive understanding of relative stability using cheaper quantum chemical methods.     

Theoretical modeling and interpretation of X-ray absorption spectra of liquid water

We report extensive calculations to examine the capability of theory to explain the XAS spectra of liquid water. Several aspects that enter the theoretical model are addressed, such as the quantum mechanical methods, the statistics and the XAS model. As input into our quantum mechanical calculations we will use structural information on liquid water obtained from first principles and from classical molecular dynamics simulations. As XAS models, we will examine the full core hole and the half core hole approximations to transition state theory. The quantum mechanics is performed on the basis of density functional theory. We conclude from this study that recent experimental results are fully consistent with, and can be completely explained by, present day theory, in particular, the pre-edge peak is reproduced. We also find that the average bond coordination in liquid water is 3.1 and that the assertion in a recent paper that the hydrogen bond number is much less than that cannot be substantiated. Our calculations emphasize that further advances in our understanding of water can only be made by more sophisticated spectroscopy with significantly increased resolution.     

The concept of the chemical bond

The concept of the chemical bond is very old. Many interpretations have been proposed. Nevertheless, the problem is far from being solved. At the present time, the chemist has the choice between two models: the Lewis model (electron pairs) and the quantum model. In spite of a current opinion, both models are not logically equivalent. The localization of molecular orbitals is only a mathematical operation which does not involve any physic localization of the electrons. The loge theory is not more satisfying owing to the fact that loges with minimal fluctuation do not exist in all molecules. The theory of orbital domains seems to bring a solution. Nevertheless, its interpretation can be obtained only outside the strict framework of quantum mechanics.     

MOLCAS 7: The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two‐electron integrals and in the generation of so‐called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self‐consistent field, density functional theory, 2nd order perturbation theory, complete‐active space self‐consistent field multiconfigurational reference 2nd order perturbation theory, and coupled‐cluster methods. The report further elaborates on the implementation of a restricted‐active space self‐consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas‐Kroll‐Hess transformation for one‐component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so‐called picture‐change‐free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Pointing the way to the products? Comparison of the stress tensor and the second-derivative tensor of the electron density

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion-approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity.     

Methods and Applications of Quantum Chemistry. Part I: Physical and Mathematical Basis

After an introduction to the fundamental concepts of quantum mechanics it is shown how to describe a chemical system in the language of theoretical physics. The equations which one obtains can not, in general, be solved in closed form. Approximate numerical methods that furnish sufficiently accurate solutions for many problems of interest are, however, available. The most important of these are presented briefly, and are given physically visualizable interpretations as far as this is possible. Special attention is devoted to more modern methods of quantum chemistry, to the basis assumptions underlying them, their scope, and their limitations. Treatment of the theory of the chemical bond is reserved for Part II.     

Matula numbers, Gödel numbering and Fock space

By making use of Matula numbers, which give a 1-1 correspondence between rooted trees and natural numbers, and a Gödel type relabelling of quantum states, we construct a bijection between rooted trees and vectors in the Fock space. As a by product of the aforementioned correspondence (rooted trees $\leftrightarrow $ ? Fock space) we show that the fundamental theorem of arithmetic is related to the grafting operator, a basic construction in many Hopf algebras. Also, we introduce the Heisenberg–Weyl algebra built in the vector space of rooted trees rather than the usual Fock space. This work is a cross-fertilization of concepts from combinatorics (Matula numbers), number theory (Gödel numbering) and quantum mechanics (Fock space).     

Excited state properties of sizable molecules in solution: from structure to reactivity

We review some recent advances in quantum mechanical methods devised specifically for the study of excited electronic state of large size molecules in solution. The adopted theoretical/computational framework is rooted in the density functional theory (DFT) and its time-dependent extension (TD-DFT) for the characterization of ground and excited states, in the polarizable continuum model (PCM) for the treatment of bulk solvent effects, and in time-dependent quantum mechanical methods for chemical dynamics. Selected applications to the simulation of absorption spectra, to the interpretation of time-resolved experiments, and to the computation of dissociative electron transfer rates are presented and discussed.     

Search for a density-based alternative quantum mechanics of many-electron systems

There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.     

A solid state 13C NMR, crystallographic, and quantum chemical investigation of chemical shifts and hydrogen bonding in histidine dipeptides

We report the first solid-state NMR, crystallographic, and quantum chemical investigation of the origins of the 13C NMR chemical shifts of the imidazole group in histidine-containing dipeptides. The chemical shift ranges for Cgamma and Cdelta2 seen in eight crystalline dipeptides were very large (12.7-13.8 ppm); the shifts were highly correlated (R2= 0.90) and were dominated by ring tautomer effects and intermolecular interactions. A similar correlation was found in proteins, but only for buried residues. The imidazole 13C NMR chemical shifts were predicted with an overall rms error of 1.6-1.9 ppm over a 26 ppm range, by using quantum chemical methods. Incorporation of hydrogen bond partner molecules was found to be essential in order to reproduce the chemical shifts seen experimentally. Using AIM (atoms in molecules) theory we found that essentially all interactions were of a closed shell nature and the hydrogen bond critical point properties were highly correlated with the N...H...O (average R2= 0.93) and Nepsilon2...H...N (average R2= 0.98) hydrogen bond lengths. For Cepsilon1, the 13C chemical shifts were also highly correlated with each of these properties (at the Nepsilon2 site), indicating the dominance of intermolecular interactions for Cepsilon1. These results open up the way to analyzing 13C NMR chemical shifts, tautomer states (from Cdelta2, Cepsilon1 shifts), and hydrogen bond properties (from Cepsilon1 shifts) of histidine residue in proteins and should be applicable to imidazole-containing drug molecules bound to proteins, as well.     

A Computational Journey across Nitroxide Radicals: From Structure to Spectroscopic Properties and Beyond

Nitroxide radicals are characterized by a long-lived open-shell electronic ground state and are strongly sensitive to the chemical environment, thus representing ideal spin probes and spin labels for paramagnetic biomolecules and materials. However, the interpretation of spectroscopic parameters in structural and dynamic terms requires the aid of accurate quantum chemical computations. In this paper we validate a computational model rooted into double-hybrid functionals and second order vibrational perturbation theory. Then, we provide reference quantum chemical results for the structures, vibrational frequencies and other spectroscopic features of a large panel of nitroxides of current biological and/or technological interest.