Screening Constants Research Articles

Polyamines. III. Spectroscopic properties of N, N-bis-(phthalimidopropyl)- N-octylamine and supramolecular interactions in its crystals

A new derivative of polyamine, N, N-bis-(phthalimidopropyl)- N-octylamine has been synthesized and its structure studied by X-ray diffraction, FTIR, 1H and 13C NMR spectroscopy. The B3LYP and DFT calculations have been carried out. The molecular conformation of N, N-bis-(phthalimidopropyl)- N-octylamine is folded and stabilized by an intramolecular C H⋯O hydrogen bond. A close similarity to the conformation of N, N-bis-(phthalimidopropyl)- N-propylamine has been found. The both molecules differ by the length of the saturated chains on the N-amine atom. The long N-octyl chain substituent gives rise to the supramolecular structure which is different to that one formed by the N-propyl derivative. The supramolecular structure is driven by weak C H⋯O and π⋯ π interactions. The optimized bond lengths as well as bond angles for N, N-bis-(phthalimidopropyl)- N-octylamine calculated by B3LYP/6-31G(d,p) approach are compared with the X-ray data. The screening constants for 13C and 1H atoms have been calculated by the GIAO/B3LYP/6-31G(d,p) approach and analyzed. Linear correlations between the experimental 1H and 13C chemical shifts and the computed screening constants have been obtained.

Microparticle Charge Screening in Non‐Equilibrium Plasmas with Two Types of Positive Ions

AbstractThe study of screening a microparticle charge in a plasma taking into account sinks of electrons and ions to the microparticle and bulk processes of their production and loss in a plasma is reported. The research objective is to investigate the effect of the conversion of atomic ions Ar+ to molecular ones Ar2+ on character of screening in a plasma with an external ionization source. It is determined that the plasma due to the ion conversion consists of two positive ion species. This circumstance leads to the three‐exponential charge screening, moreover there exists a region of plasma parameters where all the screening constants have comparable values. Numerical simulation of microparticle charging on the basis of the drift‐diffusion approach is performed and comparison of the obtained data with the analytical results is fulfilled (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Evaluation of one‐electron molecular integrals over complete orthonormal sets of Ψα ‐ETO using auxiliary functions

AbstractBy the use of expansion and one‐range addition theorems, the one‐electron molecular integrals over complete orthonormal sets of Ψα ‐exponential type orbitals arising in Hartree–Fock–Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater‐, Coulomb‐Sturmian‐, and Lambda‐type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Screening in gated bilayer graphene

The tight-binding model of a graphene bilayer is used to find the gap between the conduction and valence bands, as a function of both the gate voltage and as the doping by donors or acceptors. The total Hartree energy is minimized and the equation for the gap is obtained. This equation for the ratio of the gap to the chemical potential is determined only by the screening constant. Thus the gap is strictly proportional to the gate voltage or the carrier concentration in the absence of donors or acceptors. In the opposite case, where the donors or acceptors are present, the gap demonstrates the asymmetrical behavior on the electron and hole sides of the gate bias.

Calculation of three-center nuclear attraction integral over Slater type orbitals in molecular coordinate system using Löwdin α-radial function and Guseinov’s two-center charge density expansion formulae

Using Lowdin α-radial function and the Guseinov’s charge density expansion formulae, the calculation of the three-center nuclear attraction integrals over Slater type orbitals in molecular coordinate system is performed. The proposed algorithm is especially useful for computation of multicenter-multielectron integrals that arise in the Hartree-Fock-Roothaan approximation, which plays a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules and solids. The algorithm described in the present work is valid for the arbitrary values of quantum numbers, screening constants and internuclear distances. The calculation results are in good agreement with those obtained using the alternative evaluation procedure.

Combined theory of two- and four-component complete orthonormal sets of spinor wave functions and Slater type spinor orbitals in position, momentum and four-dimensional spaces

By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two- and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin-1/2 particles by the two- and four-component relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four-component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.

EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER–MULTIELECTRON INTEGRALS

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETO α = 1,0,-1,-2,…) introduced by the author. Three-center overlap integrals of Ψα appearing in these relations are expressed through the two-center overlap integrals between Ψα-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter–multielectron integrals occurring when the complete orthonormal sets of Ψα-ETO are used as basis functions in the Hartree–Fock–Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter–multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Ψα-orbitals.

Evaluation of Multicenter Multielectron Integrals Using One-range Addition Theorems in Terms of STOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices

Using one-range addition theorems for Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) introduced by the author, the series expansion formulae are derived for the multicenter multielectron integrals. The expansion coefficients occurring in these relations are presented through the overlap integrals of two STOs. The convergence of series expansion relations is tested by calculating concrete cases. The accuracy of the results is quite high for quantum number, screening constants and location of orbitals. The final results are especially useful in the calculation of multielectron properties for atoms and molecules when Hartree-Fock-Roothaan (HFR) and explicitly correlated methods are employed.

Computer-generated formulas for hybrid integrals over slater-type orbitals

General formulas without auxiliary functions are developed for two-center hybrid integrals over Slater-type orbitals by using an algebraic single-center expansion approach. Explicit formulas for each combination of orbitals can be generated by computer and the formula coefficients may be stored in arrays. Simple formulas result if all the orbitals have equal screening constants.

Computer-generated formulas for exchange integrals over slater-type orbitals

Formulas for two-center exchange integrals using Slater-type orbitals with equal screening constants are produced by employing computer algebra in the implementation of the Lowdin alpha function method which expands displaced orbitals in an infinite series of spherical harmonics. Our use of a C-matrix with integer elements in connection with the alpha function gives exact results for each term of an infinite series in the generated formulas. It is possible to terminate the series for the value of the exchange integral by “extrapolating to infinity” using judiciously chosen rearrangements and expansions of the formulas: as an example the Sugiura formula for 1s orbitals is produced to illustrate the technique.

Molecular screening and spectroscopic constants

The use of a semi-empirically determined orbital exponent is investigated in a 4-electron energy calculation of LiH. The results are compared to those of a 2-electron calculation by the same semi-empirical method. Selected spectroscopic constants are also calculated from the energy dependence upon internuclear distance. The semi-empirical method is found to essentially reproduce the total energy within the limitations of the approximation framework which is used. The method is not as successful in predicting the spectroscopic constants.

Study of N, N-dimethyl(carboethoxymethyl)-3-phthalimidopropylammonium chloride dihydrate by DFT calculations, NMR and FTIR spectroscopy

N, N-dimethyl(carboethoxymethyl)-3-phthalimidopropylammonium chloride dihydrate ( 1) and N, N-dimethyl(carboxymethyl)-3-phthalimidopropylammonium hydrochloride ( 3) have been obtained in reaction of N, N-dimethyl-3-phthalimidopropylamine with ethyl chloroacetate and chloroacetic acid, respectively. N, N-dimethyl(carboethoxymethyl)-3-phthalimido-propylammonium chloride dihydrate ( 1) has been characterized by FTIR and NMR spectroscopy. Moreover, for ( 1) and ( 3) B3LYP calculations have been carried out. The optimized bond lengths, bond angles and torsion angles calculated by B3LYP/6-31G(d,p) approach have been presented. Both FTIR and Raman spectra of ( 1) are consistent with the calculated structures in the gas phase. Correlations between the experimental 1H and 13C NMR chemical shifts ( δ exp) of investigated compound in D 2O, and the GIAO/B3LYP/6-31G(d,p) calculated magnetic isotropic shielding tensors ( σ calc), δ exp = a + b σ calc, are reported. The assignments of the anharmonic experimental solid state vibrational frequencies of ( 1) based on the calculated B3LYP/6-31G(d,p) harmonic frequencies have been made. Linear correlations between the experimental 1H and 13C chemical shifts and the computed screening constants confirm the optimized geometry.

Effects of substituents in the cationic and anionic η3-allylpalladium complexes according to data from 13C NMR spectroscopy and quantum chemical calculations

A linear correlation of chemical shifts (δ) of signals in the 13C NMR spectra of the unsubstituted terminal carbon atom of the allyl ligand in [(1-R-η3-C3H4)Pd]NO3 (R = Me, CH2OMe, CO2Me, COMe, CHO) with the substituent constants σ+ and σs- in acetone solutions was found. A considerable deviation from linearity was observed for R = Ph. The 13C nuclear magnetic screening constants were calculated by the DFT method in the GIAO approximation for equilibrium geometries of the cations [(1-R-η3-C3H4)Pd(Me2C=0)2]+ and anions [(1-R-η3-C3H4)PdCl2]s-. In the latter case, the theoretical and experimental δ values are consistent. The influence of the substituent R on the geometric parameters and charges on atoms in the neutral, anionic, and cationic η3-allylpalladium complexes is discussed.

COMBINED THEORY OF NONRELATIVISTIC AND QUASIRELATIVISTIC ATOMIC INTEGRALS OVER INTEGER AND NONINTEGER N-SLATER-TYPE ORBITALS

One- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The combined analytical relations in terms of these basic functions are derived for the non- and quasi-relativistic atomic integrals over integer and noninteger n-Slater-type orbitals. The relationships obtained are valid for the arbitrary values of principal quantum numbers and screening constants of Slater orbitals.

Calculation of two-center overlap integral in molecular coordinate system over Slater type orbital using Löwdin α-radial and Guseinov rotation–angular functions

By use of Lowdin and Guseinov relations for the radial and angular part of two-center overlap integrals, respectively, the computer calculations of overlap integrals over Slater type orbitals (STOs) in molecular coordinate system are performed. The results of calculations are valid for arbitrary principal quantum numbers, screening constants and location of STOs. Excellent agreement with benchmark results and stability of the technique are demonstrated.

Use of Filter-Steinborn B and Guseinov $${Q_{ns}^q}$$ auxiliary functions in evaluation of two-center overlap integrals over Slater type orbitals

An efficient method for computing overlap integral over Slater type orbitals based on the B Filter-Steinborn and Guseinov \({Q_{ns}^q}\) auxiliary functions is presented. The final results are expressed through the binomial coefficients with the help of which the overlap integrals can be evaluated efficiently and accurately. The results of calculation are in good agreement with those obtained by other method for arbitrary principal quantum numbers and different screening constants.

Theory of complete orthonormal relativistic vector wave function sets and Slater type relativistic vector orbitals in coordinate, momentum and four-dimensional spaces

The new analytical relations for the relativistic vector wave functions and Slater type relativistic vector orbitals in coordinate, momentum and four-dimensional spaces are derived using the properties of quasirelativistic vector spherical harmonics introduced by the author in previous paper (I.I. Guseinov, J. Math. Chem., 44, 197 (2008)) and complete orthonormal scalar basis sets of nonrelativistic ψ α -exponential type orbitals (ψ α -ETO), \({\phi ^{\alpha}}\)-momentum space orbitals (\({\phi ^{\alpha}}\)-MSO) and z α -hyperspherical harmonics (z α -HSH). The 6-component relativistic vector wave functions obtained are complete without the inclusion of the continuum. The relativistic vector wave function sets and Slater type relativistic vector orbitals are expressed through the corresponding quasirelativistic vector wave functions and Slater vector orbitals, respectively. The analytical formulas are also derived for overlap integrals over Slater type relativistic vector orbitals with the same screening constants in coordinate space.

Unified treatment of nonrelativistic and quasirelativistic atomic integrals over complete orthonormal sets of $${\Psi^{\alpha}}$$ -exponential type orbitals

The new one- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The general analytical relations in terms of basic functions suggested are derived for the non- and quasi-relativistic atomic integrals over complete orthonormal sets of \({\Psi ^{\alpha}}\) -exponential type orbitals introduced by the author, where α = 1,0, − 1, − 2, . . . The relationships obtained are valid for the arbitrary values of quantum numbers and screening constants of orbitals.

Investigation of 2snp±1,3Po resonances of two-electron systems using the screening constant by unit nuclear charge method

The 2snp±1,3Po doubly excited states with n⩽6 of helium-like ions are investigated using screening constant by unit nuclear charge (SCUNC). Calculations are performed for total energies, excitation energies and total Coulomb interaction energies between the two electrons in He-isoelectronic series up to Z=10. The results obtained agree with the available theoretical and experimental literature values.

Polyamines. Part II: Spectroscopic properties of N, N-dimethyl-3-phthalimidopropylammonium acetate and hydrochloride and supramolecular interactions in their crystals

N, N-Dimethyl-3-phthalimidopropylammonium acetate and hydrochloride have been characterized by X-ray diffraction, FT-IR, Raman and NMR spectroscopy. Also B3LYP and DFT calculations have been carried out. The optimized bond lengths, bond angles and torsion angles calculated by B3LYP/6-31G(d,p) approach have been compared with the X-ray data. The screening constants for 13C and 1H atoms have been calculated by the GIAO/B3LYP/6-31G(d,p) approach and analyzed. Linear correlations between the experimental 1H and 13C chemical shifts and the computed screening constants confirm the optimized geometry. The packing of the both molecules is dominated by hydrogen bonds, including the weak C H⋯O bonds. The supramolecular structure is organized into hydrophilic and hydrophobic segments.