The Ehrenfest force field: A perspective based on electron density functions.

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen-hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

Primary Photophysics of Nicotinamide Chromophores in Their Oxidized and Reduced Forms.

Nicotinamide adenine dinucleotide (NADH) is an important enzyme cofactor with emissive properties that allow it to be used in fluorescence microscopies to study cell metabolism. Its oxidized form NAD+, on the other hand, is considered to produce negligible fluorescence. In this contribution, we describe the photophysics of the isolated nicotinamidic system in both its reduced and oxidized states. This was achieved through the study of model molecules that do not carry the adenine nucleotide since its absorbance would overlap with the absorption spectrum of the nicotinamidic chromophores. We studied three model molecules: nicotinamide (niacinamide, an oxidized form without nitrogen substitution), the oxidized chromophore 1-benzyl-3-carbamoyl-pyridinium bromide (NBzOx), and its reduced form 1-benzyl-1,4-dihydronicotinamide (NBz). For a full understanding of the dynamics, we performed both femtosecond-resolved emission and transient absorption experiments. The oxidized systems, nicotinamide and NBzOx, have similar photophysics, where the originally excited bright state decays on an ultrafast timescale of less than 400 fs. The depopulation of this state is followed by excited-state positive absorption signals, which evolve in two timescales: the first one is from 1 to a few picoseconds and is followed by a second decaying component of 480 ps for nicotinamide in water and of 80-90 ps for nicotinamide in methanol and NBzOx in aqueous solution. The long decay times are assigned as the S1 lifetimes populated from the original higher-lying bright singlet, where this state is nonemissive but can be detected by transient absorption. While for NBzOx in aqueous solution and for nicotinamide in methanol, the S1 signal decays to the solvent-only level, for the aqueous solutions of nicotinamide, a small transient absorption signal remains after the 480 ps decay. This residual signal was assigned to a small population of triplet states formed during the slower S1 decay for nicotinamide in water. The experimental results were complemented by XMS-CASPT2 calculations, which reveal that in the oxidized forms, the rapid evolution of the initial π-π* state is due to a direct crossing with lower-energy dark n-π* singlet states. This coincides with the experimental observation of long-lived nonemissive states (80 to 480 ps depending on the system). On the other hand, the reduced model compound NBz has a long-lived emissive π-π* S1 state, which decays with a 510 ps time constant, similarly to the parent compound NADH. This is consistent with the XMS-CASPT2 calculations, which show that for the reduced chromophore, the dark states lie at higher energies than the bright π-π* S1 state.

Quantum dynamics of the internal motion of biphenyl-based molecular junctions.

Single molecule junctions based on selected 4,4'-biphenyldithiol and 4,4'-dicyanobiphenyl derivatives bonded to gold electrodes are analyzed from a dynamical point of view. A fully quantum mechanical description of the internal rotation of the biphenyl moiety is carried out in terms of the nuclear wavepacket dynamics obtained by the solution of the time-dependent Schrödinger equation expressed in terms of the torsion angle between the phenyl rings. The required potential energy surfaces are computed using ab initio electronic structure methods. The nature and positions of the substituents on the phenyl rings determine the features of the potential energy surfaces. The effect of the initial conditions on the time propagation of the nuclear wavepackets and, as a consequence, on the evolution of the conformational distribution is also analyzed. In addition, the conductances at zero bias for the nanojunctions were computed for different conformations of the biphenyl fragments. Weighted by the wavepacket amplitudes, non-stationary conductance expectation values, and time-averaged torsion angles and conductances for the entire simulation are obtained. The consequences of using the time-averaged values to perform a linear regression between the conductance and the square of the cosine of the dihedral angle between the phenyl rings are analyzed and compared to the usual static approach based only on the information for equilibrium geometries. The study of the time dependent conformational variations of the biphenyl moieties in the nanojunctions allows for a better understanding of the quantum chemical phenomena that affect their transport properties.

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states.

An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact Vxc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.

Control of Molecular Conformation and Crystal Packing of Biphenyl Derivatives.

This Review presents a discussion of the conformation of biphenyl derivatives in different chemical environments. The interplay between aromatic stabilization and steric repulsion, normally considered to explain the conformation of the molecule, is contrasted with the interpretation provided by models not based on molecular orbitals. The electronic control of conformation by means of appropriate hydrogen substitution is discussed by examples taken from chemistry and molecular electronics. Supramolecular synthons involving biphenyl are critically analyzed in terms of the molecular conformation, crystal packing and intermolecular forces. Some directions for future research on the control of the conformation of biphenyls are also presented.

Implementation of the interacting quantum atom energy decomposition using the CASPT2 method.

We present an implementation of the interacting quantum atom (IQA) energy decomposition scheme using the complete active space second-order perturbation theory (CASPT2). This combination yields a real-space interpretation tool with a proper account of the static and dynamic correlation that is particularly relevant for the description of processes in electronic excited states. The IQA/CASPT2 approach allows determination of the energy redistribution that takes place along a photophysical/photochemical deactivation path in terms of self- and interatomic contributions. The applicability of the method is illustrated by the description of representative processes spanning different bonding regimes: noble gas excimer and exciplex formation, the reaction of ozone with a chlorine atom, and the photodissociations of formaldehyde and cyclobutane. These examples show the versatility of using CASPT2 with the significant information provided by the IQA partition to describe chemical processes with a large multiconfigurational character.

Non-Covalent Interactions in the Biphenyl Crystal: Is the Planar Conformer a Transition State?

A combined experimental and theoretical study of the biphenyl (BP) crystal is presented. The X-ray diffraction data collected at 100 K were subjected to Hirshfeld atom and multipole refinements of the electron density, ρ(r). A theoretical exploration of the potential energy surface (PES) of the crystal was also carried out. This investigation challenges the common assumption that the planar structure of BP in the phase I crystal is an average of two twisted configurations in a double-well potential. The theoretical computations provide compelling evidence that this structure corresponds to a minimum on the PES hence to a stable molecular arrangement. Consistently, the experiment showed no evidence of positional or dynamic disorder. The intramolecular hydrogen-hydrogen bonds detected are not repulsive. The topological analysis of the experimental and theoretical ρ(r) reveals that both the intra- and intermolecular H⋅⋅⋅H and the C-H⋅⋅⋅π contacts stabilize the BP crystal.

Feynman Force Analysis of Chemical Processes in Terms of Topological Atomic Contributions.

The nature of the chemical bond is analyzed in terms of the atomic contributions to the Feynman forces using the Quantum Theory of Atoms in Molecules and the Interacting Quantum Atoms method. This approach provides a means for quantifying the relationship between the atomic electronic reorganization and the evolution of functional group interactions with the forces exerted on the nuclear framework during a chemical transformation. Using this decomposition scheme, the forces driving a chemical process are locally assigned to atoms or functional group contributions. The interatomic component of the forces can be ascribed as bonding forces; their exchange-correlation and electrostatic contributions reveal the nature of the interactions affecting the forces on the nuclei. This method is used to analyze the chemical interactions involved in the formation of ground and excited state diatomic molecules, the prototropism of formamide, the Diels-Alder cycloaddition of 1,3-butadiene with ethylene, and the Jahn-Teller effect of hydrated transition metal complexes.

Exotic Bonding Regimes Uncovered in Excited States.

Real-space tools were employed to show that the chemical bonding scenario used routinely to understand ground states lacks the necessary flexibility in excited states. It is shown that, even for two-center, two-electron bonds, the real-space bond orders have exotic values that have never been reported. The nature of these situations was uncovered by using electron-counting techniques that provide an appealing statistical interpretation of bonding descriptors, together with simple physical models. Bond orders greater than one as well as negative bond orders for a single bonding electron pair emerge in situations in which the electrons in the pair show a gregarious (bosonic) instead of the usual lonely (fermionic) behavior. In the first case the gregarious pair is intra-atomic, whereas the coupling is interatomic in the second. A number of examples are used to substantiate these claims.

Unveiling the role of intra and interatomic interactions in the energetics of reaction schemes: a quantum chemical topology analysis.

In this work we present a detailed analysis of selected reaction schemes in terms of the atomic components of the electronic energy defined by the quantum theory of atoms in molecules and the interacting quantum atoms method. The aim is to provide an interpretation tool for the energy change involved in a chemical reaction by means of the atomic and interaction contributions to the energies of the molecules involved. Ring strain in cyclic alkanes, the resonance energy of aromatic and antiaromatic molecules, local aromaticity in polycyclic aromatic hydrocarbons, intermolecular bonding in hydrogen fluoride clusters, and hydration of d-block metal dications were selected for the study. It was found that in addition to the changes in the strong C-C interactions in the carbon skeleton of the organic molecular rings, other contributions not usually considered to be important such as those between C and H atoms (either bonded or not) need to be considered in order to account for the net energy changes. The analysis unveils the role of the ionic and covalent contributions to the hydrogen bonding in HF clusters and the energetic origin and extent of cooperative effects involved. Moreover, the "double-hump" behavior observed for the hydration energy trend of [M(H2O)6]2+ complexes is explained in terms of the deformation energy of the metal cation and the increasingly covalent metal-water interactions. In addition, proper comparisons with the description provided by other methodologies are briefly discussed. The topological approach proposed in this contribution proves to be useful for the description of energy changes of apposite reaction schemes in chemically meaningful terms.

Energetic Analysis of Conjugated Hydrocarbons Using the Interacting Quantum Atoms Method.

A number of aromatic, antiaromatic, and nonaromatic organic molecules was analyzed in terms of the contributions to the electronic energy defined in the quantum theory of atoms in molecules and the interacting quantum atoms method. Regularities were found in the exchange and electrostatic interatomic energies showing trends that are closely related to those of the delocalization indices defined in the theory. In particular, the CC interaction energies between bonded atoms allow to rationalize the energetic stabilization associated with the bond length alternation in conjugated polyenes. This approach also provides support to Clar's sextet rules devised for aromatic systems. In addition, the H⋯H bonding found in some of the aromatic molecules studied was of an attractive nature, according to the stabilizing exchange interaction between the bonded H atoms. © 2017 Wiley Periodicals, Inc.

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective.

This work provides a novel interpretation of elementary processes of photophysical relevance from the standpoint of the electron density using simple model reactions. These include excited states of H2 taken as a prototype for a covalent bond, excimer formation of He2 to analyze non-covalent interactions, charge transfer by an avoided crossing of electronic states in LiF and conical interesections involved in the intramolecular scrambling in C2 H4 . The changes of the atomic and interaction energy components along the potential energy profiles are described by the interacting quantum atoms approach and the quantum theory of atoms in molecules. Additionally, the topological analysis of one- and two-electron density functions is used to explore basic reaction mechanisms involving excited and degenerate states in connection with the virial theorem. This real space approach allows to describe these processes in a unified way, showing its versatility and utility in the study of chemical systems in excited states. © 2017 Wiley Periodicals, Inc.

Electron delocalization and electron density of small polycyclic aromatic hydrocarbons in singlet excited states.

The four lowest singlet electronic states of benzene, the acenes from naphthalene to pentacene, phenanthrene and pyrene were studied by means of theoretical methods. Their vertical excitation energies from the ground electronic states were computed at the CASPT2 approximation. As an attempt to explain the trends observed in the excitation energies, several descriptors based on the electron density were used and the similarity of these molecules with their ground state counterparts was analyzed. It was found that the changes of the topological properties at the C-C bond critical points do not explain the decreasing trends for the excitation energies with the increase of the number of rings, in part because the small changes that take place in the electron density occur above and below the molecular plane. A similarity index based on electron delocalization between quantum topological atoms was defined to compare a molecule in two different electronic states. It was found that, mainly for the acenes, this index goes in line with the excitation energies to the first excited state. Implications of the changes in electron delocalization on the aromatic character of these molecules are also discussed. In general, local aromaticity decreases upon excitation.

The rotational barrier of ethane and some of its hexasubstituted derivatives in terms of the forces acting on the electron distribution.

A novel and alternative explanation of the rotational barrier of ethane and several hexasubstituted derivatives, CX3CX3 (X = H, F, CH3, Cl, Br), is suggested based on the evaluation of the properties of the electron distribution. The forces exerted on the electron density of the topological atoms making up a molecule, the Ehrenfest forces, are analyzed and, with the help of the virial theorem, they are used to explain the experimental rotational barriers. According to this approach, the barrier is mainly a consequence of the decrease of the always attractive Ehrenfest forces (EFs) linking the two C atoms. In addition, the behavior of the EFs is related to a decrease of stability of the central C atoms, which is not compensated by the stabilization of the substituents. Also, during rotation from the staggered to the equilibrium conformation, the electron density at the C-C bond critical point and the electron delocalization between C atoms decrease and are accompanied by an increase of electron delocalization between the substituents. According to the analysis of the EF field lines and to the behavior of the integrated forces, the rotational barrier cannot be explained as a result of any repulsive forces acting on the electron density, although a possible interpretation of the quantum force that balances the EF in stationary states as a measure of traditional Pauli repulsions is also examined.

Hydrogen-bond cooperative effects in small cyclic water clusters as revealed by the interacting quantum atoms approach.

The cooperative effects of hydrogen bonding in small water clusters (H2 O)n (n=3-6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ(r)) compliant with the quantum theory of atoms-in-molecules (QTAIM) and the calculation of electrostatic interactions by using one- and two-electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (Eint ) of these contorted molecules in (H2 O)n . Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of Eint for a pair of water molecules in the cluster (H2 O)n-1 become more attractive when a new H2 O unit is incorporated to generate the system (H2 O)n with the last-mentioned contribution being consistently the most important part of Eint throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω'), the QTAIM atomic charges, the topology of ρ(r), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra- and intermolecular interactions present in hydrogen-bonded systems.

Quantum molecular dynamics of the topological properties of the electron density: charge transfer in H3(+) and LiF.

This paper presents a method to analyze the time evolution of electron density descriptors defined by the quantum theory of atoms in molecules. The wave packet nuclear dynamics was followed solving the time-dependent Schrödinger equation. The time evolution of the nuclear wave packets was combined with the electronic wave functions to follow the time dependence of the average values of topological electron density descriptors. The method was applied to the reactive collision of H(+) + H(2) under different initial conditions and the photodissociation of LiF for either diabatic or adiabatic processes, with emphasis on the information provided by the time evolution of the atomic charges. These examples illustrate how this approach allows for a detailed analysis of the electronic structure in the time domain.

Application of the additivity of group energies to understand conformational preference: the anomeric effect.

The conformational preference in normal and reverse anomeric effects is analyzed by taking advantage of the known additivity and transferability of functional group energies defined by the gradient of the electron density. As the anomeric effect has an energetic origin and every change in the electron density produces an energetic change, an explanation of this phenomenon should be based on the density changes taking place in a conformational equilibrium. The total energy of substituted cyclohexanoids is partitioned into ring and substituent contributions and the preferred conformation is the result of a balance between them. This new alternative approach allows understanding of the anomeric effect in terms of group energy contributions. In general, the most stable conformer in both the anomeric and reverse anomeric effects is that where the ring transfers charge to the heteroatom in the substituent during the process.

Interpretation of vicinal proton-proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors.

The indirect vicinal proton-proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon-Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton-proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism.

Theoretical analysis of hydrogen bonding in catechol-n(H(2)O) clusters (n = 0...3).

The electronic structure and hydrogen bonding of the stable isomers of catechol and its complexes with one to three water molecules is studied by means of theoretical methods. A conformational analysis based on a simulated annealing search on the potential energy surface of each complex was carried out previous to the quantum chemical energy minimization. Twenty three stable conformers were found including some involving a pi-interaction between the catechol moiety and a water molecule. The topological properties of the electron density reveal the presence of an intramolecular hydrogen bond only in the case of one complex with three water molecules. The infrared spectra of these molecules were computed and compared to available experimental results. An alternative assignment of the experimental vibrational spectrum within the range 3340-3750 cm(-1) of the catechol-3(H(2)O) complex (M. Gerhards, C. Unterberg, and K. Kleinermanns, Phys. Chem. Chem. Phys. 2000, 2, p. 5538) is proposed. The red-shift observed for the stretching vibrational frequency of the catechol hydrogen donor hydroxyl group in the presence of water molecules is rationalized in terms of the properties of the electron distribution and a Darwinian family tree is proposed to classify the diverse structural and energetic characteristics of the stable complexes found.

Theoretical analysis of intermolecular interactions of selected residues of triosephosphate isomerase from Trypanosoma cruzi with its inhibitor 3-(2-benzothiazolylthio)-1-propanesulfonic acid.

The interaction between selected amino acid residues of the homodimeric enzyme triosephosphate isomerase from Trypanosoma cruzi with the inhibitor 3-(2-benzothiazolylthio)-1-propanesulfonic acid (BTT) was investigated by means of high level quantum chemical methods. The amino acids phe75A, arg71A and tyr102B from the enzyme monomers A and B were selected using experimental X-ray structural data. The ab initio intermolecular energies for the association of the inhibitor with the individual amino acids were calculated in two forms, namely, with a supermolecular approach and using the symmetry adapted perturbation theory. The latter also provided the contributions to the interaction energies, which were interpreted in terms of the usual van der Waals forces. The electron density for the specific interactions between BTT and the amino acids and the charge redistribution due to complex formation were also analyzed. It was found that for phe75A and tyr102B the dispersion energy is the dominant contribution to the complex stabilization followed by the induction and electrostatic energies. In addition, whereas the face-edge complex of BTT with phe75A exhibits a C-H pi bond similar to that observed for the benzene dimer, the complex with arg71A shows an important charge redistribution on the amino acid in regions far removed from those where the intermolecular specific interactions occur.