Entropic concepts in electronic structure theory

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations.     

The intermolecular interactions in the aminonitromethylbenzenes

The intermolecular non-covalent interactions in aminonitromethylbenzenes namely 2-methyl-4-nitroaniline, 4-methyl-3-nitroaniline, 2-methyl-6-nitroaniline, 4-amino-2,6-dinitrotoluene, 2-methyl-5-nitroaniline, 4-methyl-2-nitroaniline, 2,3-dimethyl-6-nitroaniline, 4,5-dimethyl-2-nitroaniline and 2-methyl-3,5-dinitroaniline were studied by quantum mechanical calculations at RHF/311++G(3df,2p) and B3LYP/311++G(3df,2p) level of theory. The calculations prove that solely geometrical study of hydrogen bonding can be very misleading because not all short distances (classified as hydrogen bonds on the basis of interaction geometry) are bonding in character. For studied compounds interaction energy ranges from 0.23 kcal mol⁻¹ to 5.59 kcal mol⁻¹. The creation of intermolecular hydrogen bonds leads to charge redistribution in donors and acceptors. The Natural Bonding Orbitals analysis shows that hydrogen bonds are created by transfer of electron density from the lone pair orbitals of the H-bond acceptor to the antibonding molecular orbitals of the H-bond donor and Rydberg orbitals of the hydrogen atom. The stacking interactions are the interactions of delocalized molecular π-orbitals of the one molecule with delocalized antibonding molecular π-orbitals and the antibonding molecular σ-orbital created between the carbon atoms of the second aromatic ring and vice versa.      

Use of the bond-projected superposition principle in determining the conditional probabilities of orbital events in molecular fragments

The problem of defining and determining the multi-conditional probabilities of many-orbital events in the chemical bond system of a molecule is addressed anew within theoretical framework of the one-determinantal orbital representation of molecular electronic structure. Its solution is vital for determining the information-theoretic indices of bond couplings between molecular fragments or the reactant/product subsystems in chemical reactions. The superposition principle of quantum mechanics, appropriately projected into the occupied subspace of molecular orbitals, is used to condition the atomic orbitals or general basis functions of the self-consistent-field calculations. The conditional probabilities between the subspaces of basis functions (atomic orbitals) are derived from an appropriate generalization of the bond-projected superposition principle. They are then used to define the triply-conditional probabilities, relating one conditional event to another. The resulting expression is shown to satisfy the relevant non-negativity and symmetry requirements. It is applied to probe the π-bond coupling in butadiene and benzene.     

A theoretical study of the intramolecular interaction between proximal atoms in planar conformations of biphenyl and related systems

The nature of the interaction between proximal hydrogens in planar biphenyl has been recently a matter of debate as arguments in favor of and against the existence of “H–H” bonding have been recently put forward. This issue is addressed here through the study of both the electron density ρ(r) and the electron localization function (ELF) η(r) obtained in quantum calculations on molecular systems with F atoms replacing hydrogens in the moiety that presents this interaction. The analysis of geometries and properties of ρ(r) and η(r) at both planar and twisted equilibrium conformations of those systems along with biphenyl, permits to get information on this intramolecular interaction that is compared with the use of the traditional chemical concepts (steric hindrance and π-resonance effects) involved. It is shown that although the ELF gives information compatible with these classical terms, this does not preclude the existence of bonds between proximal atoms with features rather similar to those of well-established intramolecular hydrogen bonds.     

Chemical Bonding in Silicon Carbonyl Complexes

Although silylene-carbonyl complexes are known for decades, only recently isolable examples have been accomplished. In this work, the bonding situation is re-evaluated to explain the origins of their remarkable stability within the Kohn-Sham molecular orbital theory framework. It is shown that the chemical bond can be understood as CO interaction with the silylene via a donor-acceptor interaction: a σ-donation from the σ_CO into the empty p-orbital of silicon, and a π-back donation from the sp² lone pair of silicon into the π*_CO antibonding orbitals. Notably, it was established that the driving force behind the surprisingly stable Si−CO compounds, however, is another π-back donation from a perpendicular bonding R−Si σ-orbital into the π*_CO antibonding orbitals. Consequently, the pyramidalization of the central silicon atom cannot be associated with the strength of the π-back donation, in sharp contrast to the established chemical bonding model. Considering this additional bonding interaction not only shed light on the bonding situation, but is also an indispensable key for broadening the scope of silylene-carbonyl chemistry.     

On interference of orbital communications in molecular systems

The atomic orbitals (AO) contributed by bonded atoms of molecular systems emit or receive the “signals” of electronic allocations to these basis functions, thus acting as the signal source (input) or receiver (output), respectively, in the associated communication network. Each orbital simultaneously participates in both the through-space and through-bridge probability propagations: the former involve direct communications between two AO while the latter are realized indirectly via orbital intermediates. This work examines the interference effects of the amplitudes of molecular probability scatterings, and introduces the operator representation of AO communications. The eigenvalue problem of the associated Hermitian operator combining the forward and reverse information propagations defines the stationary modes (“standing” waves) of the molecular propagation of electronic conditional probabilities. The combined effect of interference between the multiple (direct and indirect) information scatterings, which establishes the stationary distribution of electronic probabilities, is probed. The wave-superposition principle for the conditional-probability amplitudes of the generalized through-bridge information propagation is linked to the idempotency relations of the system density matrix. It explicitly demonstrates that the resultant effect of the probability propagations involving bridges containing all basis functions, at arbitrary bridge orders indeed generates the (stationary) molecular distribution of conditional probabilities.