Theoretical investigations of α,α,α-trifluoro-3, -p and o-nitrotoluene by means of density functional theory

This study reports the optimized molecular structures, vibrational frequencies including Infrared intensities and Raman activities, corresponding vibrational assignments, (1)H and (13)C NMR chemical shifts, the magnitudes of the JCH and JCC coupling constants, Ultraviolet-visible (UV-vis) spectra, thermodynamic properties and atomic charges of the title compounds, α,α,α-trifluoro-3, -p and o-nitrotoluene, in the ground state by means of the density functional theory (DFT) with the standard B3LYP/6-311++G(d,p) method and basis set combination for the first time. Theoretical vibrational spectra were interpreted by normal coordinate analysis based on scaled density functional force field. The results show that the vibrational frequencies and chemical shifts calculated were obtained to be in good agreement with the experimental data. Based on the comparison between experimental results and theoretical data, the calculation level chosen is powerful approach for understanding the identification of all the molecules studied. In addition, not only were frontier molecular orbitals (HOMO and LUMO), molecular electrostatic potential (MEP) and electrostatic potential (ESP) simulated but also the dipole moment, softness, electronegativity, chemical hardness, electrophilicity index, transition state and energy band gap values were predicted. According to the investigations, all compounds were found to be useful to bond metallically and interact intermolecularly; however, the thermodynamic properties confirm that the α,α,α-trifluoro-p-nitrotoluene was more reactive and more polar than the others.     

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.     

Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using M?ller-Plesset-type (MP) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, self-consistency can be neglected since the long-range correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, self-consistency effects are found to be much smaller than long-range correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the short-range energy functional term while freezing its functional derivative, namely, the short-range local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.     

Wilhelm Ostwald’s energetics 3: energetic theory and applications,part II

This is the third of a series of essays on the development and reception of Wilhelm Ostwald’s energetics. The first essay described the chemical origins of Ostwald’s interest in the energy concept and his motivations for seeking a comprehensive science of energy. The second essay and the present one discuss his various attempts, beginning in 1891 and extending over almost 3 years, to develop a consistent and coherent energetic theory. A final essay will consider reactions to this work and Ostwald’s replies, and will also seek to evaluate his program of research. Ostwald’s project—to reconstruct physics and chemistry “as a pure energetics”—is worth attending to for several reasons: first, because Ostwald did ground-breaking work in chemistry (he was awarded a Nobel Prize in 1909 for his studies in catalysis and rates of reaction); second, because an important school of physical chemistry formed around him at Leipzig, a school that promoted his ideas; and, finally, because he was a prominent and vigorous participant in debates at the end of the nineteenth century concerning the proper course of physical theory.

Paired-permanent approach to valence bond theory

A new function called paired-permanent is defined and widely discussed, and a practicable procedure for evaluations of paired-permanents is proposed, which is similar to the Laplace method for determinants. Using the concept of paired-permanents, an efficient algorithm is presented for evaluating the Hamiltonian and overlap matrix elements in the spin-free form of valence bond (VB) theory. With the new algorithm, a spin-free wavefunction is simply written as a paired-permanent, and an overlap matrix element may be obtained by evaluating a corresponding paired-permanent. Meanwhile, the Hamiltonian matrix element is expressed in terms of the summation of the products of electronic integrals and the corresponding sub-paired-permanents     

Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.     

Introducing the γ function in quantum theory

Through a series of postulates, we define a function γ(x) whose square acts as Dirac's δ(x) and exhibits several unusual properties. Though the square root of δ cannot be defined among distributions, it appears in quantum theory if one wants to associate a wave function to a (quasi)classical particle having charge distribution δ(x) . The newly defined function γ(x) serves to describe quasi-classical particles using part of the quantum formalism (eg, wave functions, operators, expectation values) but exhibiting classical properties. The function γ(x) appears to be useful to define model wave functions for simple (quasi)quantum systems. In a spherical coordinate system, γ(r − r₀) leads to a quasi-classical “bubble” model of the hydrogen atom, where the electron is distributed on the surface of a sphere with radius r₀, and it provides exact quantum mechanical energies of its total symmetric levels. For other simple quantum systems, it provides approximate but meaningful energies. In particular, exact energy differences for harmonic oscillator levels are obtained, with the zero-point energy missing.     

Improved third-order Møller-Plesset perturbation theory

Based on a partitioning of the total correlation energy into contributions from parallel‐ and antiparallel‐spin pairs of electrons, a modified third‐order Møller–Plesset (MP) perturbation theory is developed. The method, termed SCS–MP3 (SCS for spin‐component‐scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third‐order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C₂₀ isomers, transition states) demonstrate that the SCS–MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529–1537, 2003     

Integrating pharmacophore mapping,virtual screening,density functional theory,molecular simulation towards the discovery of novel apolipoprotein (apoE ε4) inhibitors

AimAn integrated protocol of virtual screening involving molecular docking, pharmacophore probing, and simulations was established to identify small novel molecules targeting crucial residues involved in the variant apoE ε4 to mimic its behavior as apoE2 thereby eliminating the amyloid plaque accumulation and facilitating its clearance.Materials and MethodsAn excellent ligand-based and structure-based approach was made to identify common pharmacophoric features involving structure-based docking with respect to apoE ε4 leading to the development of apoE ε4 inhibitors possessing new scaffolds. An effort was made to design multiple-substituted triazine derivatives series bearing a novel scaffold. A structure-based pharmacophore mapping was developed to explore the binding sites of apoE ε4 which was taken into consideration. Subsequently, virtual screening, ADMET, DFT searches were at work to narrow down the proposed hits to be forwarded as a potential drug likes candidates. Further, the binding patterns of the best-proposed hits were studied and were forwarded for molecular dynamic simulations of 10 ns for its structural optimization.ResultsSelectivity profile for the most promising candidates was studied, revealing significantly C13 and C15 to be the most potent compounds. The proposed hits can be forwarded for further study against apoE ε4 involved in neurological disorder Alzheimer’s.     

A theoretical study of CO adsorption on gold by Hückel theory and density functional theory calculations

It is crucial to understand the nature of CO adsorption on gold so as to elucidate the mechanism of low-temperature CO oxidation on nanogold catalysts. We performed theoretical analysis of CO adsorption on gold by using Hückel theory and density functional theory (DFT) calculations. Hückel theory indicates that CO adsorption on gold is dominated by the electron distribution at the Au atom, which is greatly affected by neighboring Au atoms, coadsorbed or doping species. The increase of σ-bonding electrons should weaken the CO adsorption, while the increase of π-electrons should strengthen the adsorption. DFT calculations proved this prediction quantitatively for various systems, including CO adsorption on a Au(100)-hex surface with locally varying subsurface configurations and CO coadsorption with acceptor or donor species.     

A new theory for symmetric orbital and tensor

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Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

What I like about Hückel theory

We start with some biographical notes on Erich Hückel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Hückel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. M?bius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schr?dinger equation, but as a way towards the understanding of some aspects of the Chemical Bond.     

Structural,torsional, vibrational and response electric properties of 2,2′-bitellurophene rotamers. An ab initio and density functional theory investigation

The molecular structure, conformational behaviour, vibrational spectra and electronic (hyper)polarizabilities of tellurophene and 2,2′-bitellurophene rotamers were determined in gas by correlated ab initio and density functional theory calculations. The torsional potential for the rotation around the C²–C^2′ inter-ring bond shows two minima corresponding to anti-gauche and syn-gauche structures and three maxima to planar anti and syn forms and to perpendicular conformation. The potential energy curve is rather flat over the entire 0°–180° twisting range and free rotation cannot be excluded. The IR and Raman spectra of the gauche structures are rather similar to each other, vibrational transitions being scarcely helpful for an unambiguous identification of the rotamers. The dipole moment and the first-order hyperpolarizability increase on passing from the anti-gauche to the syn-gauche conformation by a factor of five and four, respectively. The second harmonic generation nonlinear optical process can be useful to identify the 2,2′-bitellurophene rotamers. On the other hand, the electronic polarizabilities of these structures are much more closer to each other, being predicted to be within 2–13 %.