A prediction model for the properties of alkylsilanes based on the additivity of energy contributions

Based on the similarity of subgraphs in the molecular graphs of a homological series of SiH₄-SiC₈H₂₀ alkylsilanes a 22-constant additive scheme is obtained for the calculation of their physicochemical properties. By the example of SiH₄-SiC₈H₂₀ alkylsilanes it is shown that for each alkylsilane molecule the sum of numbers of simple and complex heterochains equals a triangular number. A least squares method is applied to determine the numerical values of the parameters of the scheme for the calculation of Δ _f H _{gas,298 K} ⁰ for alkylsilanes (SiC _n H_2n+4).     

Graph model for calculating the properties of saturated monoalcohols based on the additivity of energy terms

A 16-constant additive scheme was derived for calculating the physicochemical properties of saturated monoalcohols CH₄O-C₉H₂₀O and decomposing the triangular numbers of the Pascal triangle based on the similarity of subgraphs in the molecular graphs (MGs) of the homologous series of these alcohols. It was shown, using this scheme for calculation of properties of saturated monoalcohols as an example, that each coefficient of the scheme (in other words, the number of methods to impose a chain of a definite length i ₁, i ₂, … on a molecular graph) is the result of the decomposition of the triangular numbers of the Pascal triangle. A linear dependence was found within the adopted classification of structural elements. Sixteen parameters of the schemes were recorded as linear combinations of 17 parameters. The enthalpies of vaporization L _{298 K}⁰ of the saturated monoalcohols CH₄O-C₉H₂₀O, for which there were no experimental data, were calculated. It was shown that the parameters are not chosen randomly when using the given procedure for constructing an additive scheme by decomposing the triangular numbers of the Pascal triangle.     

The construction of graph models for calculations of the properties of substitution isomers of basis structures on the basis of additivity of energy contributions

A method for the construction of additive models for calculations of the properties of substitution isomers of basis structures is described for the example of a series of X-substituted methylsilanes CH_{3 − k} X _k -SiH_{3 − l} X _l (where X = CH₃, F, Cl, …, k, l = 0, 1, 2, 3). The method is based on similarity of subgraphs in graphs of several molecules and the arrangement of polygonal numbers (triangular, tetrahedral) of the Pascal triangle. Parameters taking into account multiple nonvalence interactions (-C-Si<, >C-Si<, …) through two atoms along the molecular chain of an X-substituted methylsilane (X = CH₃) were for the first time explicitly included in the calculation scheme. Taking these interactions into account allows us to completely differentiate all the structural isomers of certain molecules and obtain numerical parameter values for predicting properties P under consideration in various approximations. Numerical calculations of Δ_f H _{g,298 K}^o were performed for 16 alkylsilanes (as X-substituted methylsilanes), including 7 compounds not studied experimentally.     

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A new approach has been developed for calculating the properties of mixtures based on an equation of state explicit in reduced Helmholtz energy. This approach allows for the representation of the thermodynamic properties over a wide range of fluid states and is based on highly accurate equations of state for the pure components combined at the reduced temperature and density of the mixture. The reducing parameters used for temperature and density depend on composition. For simple mixtures (those that closely follow Raoult's law), a very accurate representation of all thermodynamic properties has been achieved with relatively simple functions. For nonideal mixtures, the reducing functions for density and temperature were modified, and a departure function was added to the equation of state. Generally, the model is able to represent liquid and vapor states with uncertainties of 0.1% in density, 1% in heat capacities and 1% in bubble point pressures if experimental data of comparable uncertainties exist. Two applications of the mixture model concepts were developed independently by the authors in the United States and Germany over the same time period. These applications include the development of individual equations for each binary system and a generalization of the model which is valid for a wide variety of mixtures. The individual approaches are presented with an explanation of the similarities and differences. Although the paper focuses mainly on binary systems, some results for ternary mixtures are also presented.     

A method for calculating the Gibbs energy of nonspecific solvation

A method for calculating the Gibbs energy of nonspecific solvation of nonelectrolytes was suggested. The new equation for the Gibbs energy of nonspecific solvation contains one solvent parameter that characterize nonspecific solvent-solute interactions and two experimental Gibbs energies of solvation in two standard solvents. The method is applicable to a wide range of solutes and solvents. It was successfully used to describe some 800 Gibbs energies of solvation for systems without specific solvent-solute interactions.     

Effective potential model for calculating the energy shift in the ground state of two-electron atoms

An effective operator for the electron–electron interaction derived earlier has been shown to be successful for calculating the ground-state energy shift values for 10 members of the helium isoelectronic sequence in terms of a single free parameter. Some possible applications of the modified interaction operator for semiempirical calculations are suggested.     

Hopfield neural network model for calculating the potential energy function from second virial data

The calculation of the intermolecular potential from the second virial coefficient is treated here by using a Hopfield neural network model. From simulated data for the prototype system HeNe, the repulsive potential was obtained with a desired accuracy. The algorithm used here is general, as it can handle noise in the experimental data and, a neural network of higher dimension can be easily constructed. Although the inversion of the short-range part of the potential was obtained in the present work, the Hopfield neural network under consideration can equally be used to invert virial data to give the long-range part of the potential. The convergence of the states of the neuron and the accuracy of the inverted potential is also discussed.     

Efficient method for calculating the resonance energy expression of benzenoid hydrocarbons based on the eunumeration of conjugated circuits

To reduce the calculating time for the summations over linearly independent and minimal conjugated circuits of benzenoid hydrocarbons (BHs), an approximate method is proposed that counts only the numbers of the first four classes of conjugated circuits R1, R2, R3, and R4, respectively. By representation of BHs as custom-made "ring-block chains" and use of the techniques of Database and visual computing, an application software is realized that is much faster and more powerful than the old one based on an enumeration technique.     

Use of cluster expansion techniques in quantum chemistry. A linear response model for calculating energy differences

In this paper we have reviewed the theoretical framework of the coupled-cluster (cc) based linear response model as a tool for directly calculating energy differences of spectroscopic interest like excitation energy (ee), ionisation potential (ip) or electron affinity (ea). In this model, the ground state of a many-electron system is described as in a coupled cluster theory for closed shells. The electronic ground state is supposed to interact with an external photon field of frequencyw, and the poles of the linear response function as a function ofw furnish with the elementary excitations of the system. Depending on the general form of the coupling term chosen, appropriate difference energies like ee, ip or EA may be generated. Pertinent derivations of the general working equations are reviewed, and specific details as well as approximations for ee, ip or ea are indicated. It is shown that the theory bears a close resemblance to the equation of motion (eom) method but is superior to the latter in that the ground state correlation is taken to all orders and may be looked upon as essentially a variant of renormalisedtda. A perturbative analysis elucidating the underlying perturbative structure of the formulation is also given which reveals that the theory has a hybrid structure: the correlation terms are treated akin to an open shellmbpt, while the relaxation terms are treated akin to a Green function theory. A critique of the methodvis-a-vis other cc-based approaches for difference energies forms the concluding part of our review.     

A solvolysis model for 2-chloro-2-methyladamantane based on the linear solvation energy approach

Solvolysis/dehydrohalogenation rates of 2-chloro-2-methyladamantane (CMA) in 15 hydrogen-bond acidic and/or basic solvents are studied. The rates of reaction in these solvents have been correlated with the solvation equation developed by Kamlet, Abraham, and Taft. The linear solvation energy relationship (LSER) derived from this study is given by the following equation: log k = -5.409 + 2.219 + 2.505alpha(1) - 1.823beta(1) where , alpha(1), and beta(1) are the solvation parameters that measure the solvent dipolarity/polarizability, hydrogen-bond acidity (electrophilicity), and hydrogen-bond basicity (nucleophilicity). A high correlation coefficient (r = 0.996, SD = 0.191) was achieved. The cavity term, which includes the Hildebrand parameter for solvent cohesive energy density, delta(H), was not found to be statistically significant for this reaction substrate. The resulting equation allows calculated rates of reaction in other solvents and provides insight into the reaction pathway. In a previously reported correlation for another tertiary chloride, tert-butyl chloride (TBC), the coefficients for alpha(1) and are significantly larger and the coefficient for is statistically significant. In addition, the coefficient for beta(1) in the TBC correlation is positive, rather than negative, indicating that the transition states for TBC and CMA are significantly different. These results demonstrate why the uses of simple solvolytic correlation methods may be invalid even for comparisons of similar type substrates, e.g., tertiary chlorides. Also, these results provide confidence in the use of multiple linear regression analysis for predicting solvolytic rates in additional solvents.     

A model for the free energy of adsorption on low energy surfaces.

In constructing a generalized thermodynamics for the fluid-vapor-solid equilibrium in poorly wetted systems the specific free energy of adsorption at saturation vapor pressure is a basic and elusive term. If the adsorbed phase is modeled as a two dimensional gas, systems for which a complete spectrum of data is available can serve as an empirical basis for constructing and testing adsorption-contact angle relationships. From the extension of such relationship other often inassessible terms can be estimated. Such a construct is reported here and extended to the estimation of the excess adsorption entropy at saturation vapor pressure in non-wetting systems     

A simple scheme for calculating the energy levels and the spectra of molecular crystals

A simple matrix method for calculating the vibrational and electron energy levels and spectra in molecular crystals is proposed.     

A minicomputer program based on additivity rules for the estimation of 13c-nmr chemical shifts

A minicomputer program for the estimation of ¹³C-n.m.r. chemical shifts based on simple additivity rules is described.     

A numerically stable procedure for calculating Møller-Plesset energy derivatives,derived using the theory of Lagrangians

Summary When Møller-Plesset energy derivatives are determined in the canonical Hartree-Fock basis, singularities or instabilities may arise due to degeneracies among the occupied or unoccupied orbitals. If a non-canonical basis is used these singularities disappear. Numerically stable expressions are presented for the molecular gradient and Hessian of the second-order Møller-Plesset energy, obtained by differentiating a fully variational Lagrangian of the energy constructed in a non-canonical representation. By using a non-canonical representation, singularities and instabilities are avoided, and the variational property of the Lagrangian ensures that Wigner's 2n + 1 rule is satisfied for the orbital derivatives and that the multipliers satisfy the stronger 2n + 2 rule. It is shown that the most expensive step in the calculation of the Hessian scales as Mn ₄o, where M is the number of independent Cartesian distortions, n the total number of orbitals, and o the number of occupied orbitals.     

A highly efficient hybrid method for calculating the hydration free energy of a protein

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three‐dimensional reference interaction site model (3D‐RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D‐RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.     

A density functional theory based estimation of the anharmonic contributions to the free energy of a polypeptide helix

We have employed density functional theory to determine the temperature dependence of the intrinsic stability of an infinite poly-L-alanine helix. The most relevant helix types, i.e., the α- and the 3(10)-helix, and several unfolded conformations, which serve as reference for the stability analysis, have been included. For the calculation of the free energies for the various chain conformations we have explicitly included both, harmonic and anharmonic contributions. The latter have been calculated by means of a thermodynamic integration approach employing stochastic Langevin molecular dynamics, which is shown to provide a dramatic increase in the computational efficiency as compared to commonly employed deterministic molecular dynamics schemes. Employing this approach we demonstrate that the anharmonic part of the free energy amounts to the order of 0.1-0.4 kcal/mol per peptide unit for all analysed conformations. Although small, the anharmonic contribution stabilizes the helical conformations with respect to the fully extended structure.     

A modified Hückel method for calculating ring current contributions to the diamagnetic susceptibilities of conjugated hydrocarbons

SCF calculations of the ring current contributions to the diamagnetic susceptibilities of certain conjugated hydrocarbons are compared with the Hückel values. It is shown that discrepancies arise because of the inherent inability of the Hückel formalism to allow for two-electron terms in the Hamiltonian. A modified Hückel scheme is proposed which rectifies this omission while still retaining the fundamental simplicity of the theory.

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Zusammenfassung Der Anteil des Ringstroms an der diamagnetischen Suszeptibilität konjugierter Kohlenwasserstoffe wurde mit der SCF-MO-Methode berechnet und mit den mittels Hückelmethode erhaltenen verglichen. Es wird gezeigt, daß die Unterschiede daher rühren, daß im Hückelformalismus die Zweielektronenterme des Hamiltonoperators nicht richtig berücksichtigt sind. Ein modifiziertes Hückelschema, das diese Terme berücksichtigt, aber die fundamentale Einfachheit der Theorie beibehält, wird angegeben.

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Résumé La contribution des courants cycliques à la susceptibilité diamagnétique des hydrocarbures conjugués est calculée par la méthode SCF-MO et comparée avec les valeurs obtenues par la méthode de Hückel. On montre que les désaccords proviennent de l'inaptitude propre au formalisme de Hückel de tenir compte des termes biélectroniques contenus dans l'hamiltonien. On propose une méthode de Hückel modifiée qui corrige cette omission tout en conservant la simplicité de la théorie.