Correspondence between the reaction force minimum and the onset of abrupt variations of the kinetic and potential energies in bond dissociation and formation.

CONTEXT: We demonstrate that the minimum of the reaction force curve of a diatomic or polyatomic molecule undergoing bond dissociation is significant in several respects. As has been pointed out in the past, it is the point at which the force opposing dissociation is strongest. It marks the boundary between the primarily structural stage of a bond dissociation (stretching) and the transition region between the stretched bond and independent atoms. We now show that the reaction force minimum is also where the kinetic and potential energy curves tend to change direction abruptly. At this point, the total energy E(R) has increased by about 27% of the dissociation energy, for both diatomic and polyatomic molecules. METHODS: Dissociation curves are analyzed at the UHF/daug-cc-pV5Z level of theory using Gaussian 16.

What Is Heat? Can Heat Capacities Be Negative?

In the absence of work, the exchange of heat of a sample of matter corresponds to the change of its internal energy, given by the kinetic energy of random translational motion of all its constituent atoms or molecules relative to the center of mass of the sample, plus the excitation of quantum states, such as vibration and rotation, and the energy of electrons in excess to their ground state. If the sample of matter is equilibrated it is described by Boltzmann's statistical thermodynamics and characterized by a temperature T. Monotonic motion such as that of the stars of an expanding universe is work against gravity and represents the exchange of kinetic and potential energy, as described by the virial theorem, but not an exchange of heat. Heat and work are two distinct properties of thermodynamic systems. Temperature is defined for the radiative cosmic background and for individual stars, but for the ensemble of moving stars neither temperature, nor pressure, nor heat capacities are properly defined, and the application of thermodynamics is, therefore, not advised. For equilibrated atomic nanoclusters, in contrast, one may talk about negative heat capacities when kinetic energy is transformed into potential energy of expanding bonds.

Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties.

Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius' virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius' virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law's evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.

A Simple Effective Δ SCF Method for Computing Optical Gaps in Organic Chromophores.

Photoluminescence effects in organic chromophores are of significant importance and requires precise description of low lying excited states. In this communication, we put forward an alternative time-independent DFT scheme for computing lowest single-particle excitation energy, especially for singlet excited state. This adopts a recently developed "virial"-theorem based model of singlet-triplet splitting which requires a DFT calculation on closed shell ground state and a restricted open-shell triplet excited state, followed by a simple 2 e - integral evaluation. This produces vertical excitation energies in small molecules, linear and non-linear polycyclic aromatic hydrocarbon and organic dyes in comparable accuracy to the TDDFT. We also explore the functional dependency of present method with three different functionals (B3LYP, wB97X and CAM-B3LYP) for polyenes and linear acenes. A systematic comparison with literature value illustrates the validity and usefulness of the present scheme in determining optical gap with fair computational cost.

Role of electronic kinetic energy and resultant gradient information in chemical reactivity.

The role of resultant gradient-information concept, reflecting the kinetic energy of electrons, in shaping the molecular electronic structure and reactivity preferences of open reactants is examined. This quantum-information descriptor combines contributions due to both the modulus (probability) and phase (current) components of electronic wavefunctions. The importance of resultant entropy/information concepts for distinguishing the bonded (entangled) and nonbonded (disentangled) states of molecular fragments is emphasized and variational principle for the minimum of ensemble-average electronic energy is interpreted as a physically equivalent rule for the minimum of resultant gradient-information, and the information descriptors of charge-transfer (CT) phenomena are introduced. The in situ reactivity criteria, represented by the populational CT derivatives of the ensemble-average values of electronic energy or resultant information, are mutually related, giving rise to identical predictions of electron flows in the acid(A) - base(B), reactive systems. The virial theorem decomposition of electronic energy is used to reveal changes in the resultant information content due to the chemical bond formation, and to rationalize the Hammond postulate of reactivity theory. The complementarity principle of structural chemistry is confronted with the regional hard (soft) acid and bases (HSAB) rule by examining the polarizational and relaxational flows in such acceptor-donor reactive systems, responses to the external potential and CT displacements, respectively. The frontier-electron basis of the HSAB principle is reexamined and the intra- and inter-reactant communications in A-B systems are explored.

Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials.

The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tensor and identify the assumptions and misinterpretations that lead to its symmetric property. We then make a direct measurement of the stress tensor in molecular dynamics simulations of four different material systems using the physical definition of stress as force per unit area acting on surface elements. Simulation results demonstrate that the stress tensor is asymmetric near dislocation cores, phase boundaries, holes and even in homogeneous material under a shear loading. In addition, the atomic virial stress and Hardy stress formulae are shown to significantly underestimate the stress tensor in regions of stress concentration.

On Atoms-in-Molecules Energies from Kohn-Sham Calculations.

Herein, we discuss three methods to partition the total molecular energy into additive atomic contributions within the framework of Bader's atoms-in-molecules theory and in the particular context of Kohn-Sham density functional theory. The first method is derived from the virial theorem, whereas the two other schemes, termed "standard" and "model", are based on Pendás' interacting-quantum-atoms decomposition. The methods are then compared for a dataset of molecules of interest for direct application in organic chemistry and biochemistry. Finally, the relevance of the three methods for the prediction of intrinsic reactivity properties (e.g., electrophilicity) or for unravelling the nature of chemical bonding (e.g., in halogen bonds, beyond the pure electrostatic point of view), is examined and paves the way for their more systematic use for the in silico design of new reactants.