Oktay Sinanoğlu

Theory of Dissociation Pressures of Some Gas Hydrates

Dissociation pressures of some gas hydrates have been evaluated using the Lennard‐Jones 12–6, 28–7, and Kihara potentials in the Lennard‐Jones‐Devonshire cell model. The Lennard‐Jones 28–7 potential gives the least satisfactory results. The Lennard‐Jones 12–6 potential works satisfactorily for the monatomic gases and CH4 but poorly for the rodlike molecules C2H6, CO2, N2, O2, C2H4. This failure may be due to (i) distortions of the hydrate lattice, (ii) neglect of molecular shape and size in determining the cavity potential (iii) barrier to internal rotation of the molecule in its cavity. A crude model for the lattice shows that it is not distorted. The Kihara potential predicts better dissociation pressures for the hydrates of the rodlike molecules. Unlike the previously used Lennard‐Jones 12–6 potential, it depends on the size and shape of the interacting molecules. The absence of lattice distortions, improved dissociation pressures through the use of the Kihara potential and the restriction of the motio...

Microscopic surface tension down to molecular dimensions and microthermodynamic surface areas of molecules or clusters

Surface tension, surface energy, and entropy of small droplets, n clusters, and of cavities in liquids for sizes down to a single molecule are obtained. Rigourous relations are derived that relate microsurface properties to the usual handbook properties of bulk liquids. The microvalues and their dependence on the ratio of the cluster, droplet, or cavity size to the average liquid molecular size are given for common solvents, polar and nonpolar, including alcohols, water, hydrocarbons, rare gas liquids, and liquid (or solid) metals. Microscopic values are less than bulk‐planar values by around 40% for nonpolar liquids, and greater for polar liquids by around 60%. The n‐cluster (or cavity) sizes ? at which the microsurface properties approach the bulk values within a desired percentage, e.g., 5%, are given. The ordinary, bulk thermodynamic properties of liquids are also related to new useful quantities: ’’microthermodynamic surface areas’’ of molecules from which, using the equations given, ’’experimental’’...

Effective Intermolecular Pair Potentials in Nonpolar Media

Using third‐order perturbation theory, effective London dispersion forces between two molecules in a medium are evaluated. The reduction in the pair interaction is calculated for spherical and polymeric bodies at various separations. For nearest neighbors in pure liquids, pair potentials decrease by 1.8% in helium, and 32% in carbon tetrachloride. The contribution to the total energy of the liquid is one‐third of this. The dispersion forces between lateral base pairs in a single DNA double helix decrease by about 28% due to third‐ and fourth‐order perturbations involving the four neighboring bases of each pair. Solvent effects cause an additional decrease of 14% (in water) to 18% (in formamide). The guanine‐cytosine and adenine‐thymine pairs change similarly. In general between segments of any two typical linear polymer chains (ionization potential of 10 V), dispersion forces decrease between 17% and 22% in water. In the theoretical sections, operator and diagrammatic techniques are presented which simpli...

Inter- and Intra-Atomic Correlation Energies and Theory of Core-Polarization

Atomic and molecular energies depend strongly on the correlation in the motions of electrons. Their complexity necessitates the treatment of a chemical system in terms of small groups of electrons and their interactions, but this must be done in a way consistent with the exclusion principle. To this end, a nondegenerate many‐electron system is treated here by a generalized second‐order perturbation method based on the classification of all the Slater determinants formed from a complete one‐electron basis set. The correlation energy of the system is broken down into the energies of pairs of electrons including exchange. Also some nonpairwise additive terms arise which represent the effect of the other electrons on the energy of a correlating pair because of the Pauli exclusion principle. All energy components are written in approximate but closed forms involving only the initially occupied H.F. orbitals. Then each term acquires a simple physical interpretation and becomes adoptable for semiempirical usage....

Group theoretic prediction of configuration mixing effects due to Coulomb repulsions in atoms with applications to doubly‐excited spectra

A group theoretical method which predicts Coulomb repulsion mixing coefficients of doubly−excited atomic states is presented. Good agreement with calculated mixings in helium is found. Two new quantum numbers and three rules classify and predict the energy level orderings. The exact mathematical construction of 1/r12 in the group theoretical configuration−mixed basis is given. It leads naturally to a formulation of the corresponding many−electron problem of configurational mixings.

Many‐Electron Theory of Atoms and Molecules. III. Effect of Correlation on Orbitals

The exact wavefunction of an N‐electron atom or molecule contains, after the Hartree‐Fock (HF) part, correlation terms involving successively one, two, … N electrons at a time. Particularly in closed shells, one‐electron terms fi result mainly from pair correlations. The fi were previously neglected in the many‐electron theory. Reasons for the smallness of fi are summarized. Different types of correlation effects are classified, and methods for estimating each type of fi are given. fi in closed form, i.e., including infinitely many single excitations is less than 2.8% of the Hartree‐Fock orbital in He with an energy contribution 0.0001 a.u. (63 cal/mole). In the H2 molecule fi is negligible for (R/Re) <2. At larger R, as (1σg)2 becomes degenerate with (1σu)2 the fi effect increases to ∼0.4 eV at dissociation. However, in such cases and in actual nonclosed shells, these nondynamical fi are removed if HF orbitals are obtained after the removal of degeneracies. Dynamical correlation effects give negl...

Intermolecular‐Potential‐Energy Curves—Theory and Calculations on the Helium—Helium Potential

Calculation of intermolecular‐potential‐energy curves by the application of the many‐electron theory of atoms and molecules is outlined. The interaction is split into a Hartree—Fock and a correlation part. Both parts are given both in localized and in MO descriptions. Most of the interaction is calculated directly, not by difference of total energies. The correlation part involves only two‐electron variational equations. These results are then used to obtain the many‐electron contributions. To examine the method and estimate the magnitude of the various contributions, the helium—helium interaction is calculated for distances over 4.5 a.u. (experimental minimum about 5.5 a.u.) using a very simple localized molecular wavefunction based on single Slater atomic orbitals. The correlation‐energy contribution is calculated with the Hirschfelder‐Linnett pair function previously used for hydrogen interactions. Many‐electron and distortion effects contribute 29% of the correlation part at the potential minimum (Re)...

Correlations between tetrahedrally localized orbitals

Abstract It is shown that correlations between neighboring tetrahedral orbital contribute about twice as much to the valence shell correlation energies of neon and methane, as the correlations within the four doubly occupied (“bonds”) tetrahedral pairs. “Non-bonded attractions” are thus not negligible but may be an important part of the correlation energies of saturated molecules.

1‐ and 2‐topology of reaction networks

The kinds of reaction networks introduced earlier by this writer are capable of diverse applications in chemical physics, biochemistry, chemical engineering, economics, ecological, and other dynamics. All possible mechanisms or pathways as a function of the numbers of reaction steps ρ or species σ are generated with them. They also give the rate laws, multiplicity of steady states, the nature of their dynamic instabilities, oscillations, etc. These properties are related to a large extent on the 1‐ and 2‐topology of the networks, {N}. The {N} are graphs of two kinds of lines and two kinds of vertices. They can be planar or nonplanar. The genus t and thickness t of any N are related to ρ, σ and the numbers of catalytic and autocatalytic cycles. The Betti numbers Bi(p) of 1‐ and 2‐complexes constituted by N and other topological invariants of the networks under two kinds of homeomorphisms are given. A number of theorems are stated and proved. The above reaction networks are interesting mathematical objects in that they help classify coupled nonlinear differential equations.The kinds of reaction networks introduced earlier by this writer are capable of diverse applications in chemical physics, biochemistry, chemical engineering, economics, ecological, and other dynamics. All possible mechanisms or pathways as a function of the numbers of reaction steps ρ or species σ are generated with them. They also give the rate laws, multiplicity of steady states, the nature of their dynamic instabilities, oscillations, etc. These properties are related to a large extent on the 1‐ and 2‐topology of the networks, {N}. The {N} are graphs of two kinds of lines and two kinds of vertices. They can be planar or nonplanar. The genus t and thickness t of any N are related to ρ, σ and the numbers of catalytic and autocatalytic cycles. The Betti numbers Bi(p) of 1‐ and 2‐complexes constituted by N and other topological invariants of the networks under two kinds of homeomorphisms are given. A number of theorems are stated and proved. The above reaction networks are interesting mathematical objects ...

Denaturation of proteins in methanol/water mixtures

The solvophobic theory developed earlier by Sinanoglu introducing the use of molecular surface areas and microthermodynamic surface and interfacial tensions at molecular dimensions is applied to the interpretation of calorimetric data on denaturation of lysozyme in a wide range of methanol/water mixtures. The experimental values of standard unitary free energies of denaturation correlate well with our predictions. The molecular surface area change of the protein upon denaturation is evaluated using the solvophobic theory. The maximum in the stability of the native form of the protein is predicted to occur at 8% (v/v) methanol. This is found to be in agreement with the experimental results.