Evaluation of overlap integrals with integer and noninteger n Slater-type orbitals using auxiliary functions

The series expansion formulae are derived for the overlap integrals with arbitrary integer n and noninteger n* Slater-type orbitals (ISTOs and NISTOs) in terms of a product of well-known auxiliary functions A(sigma) and B (k). The series becomes an ordinary closed expression when both principal quantum numbers n* and n'* of orbitals are integer n*= n and n'*= n'. These formulae are especially useful for the calculation of overlap integrals for large quantum numbers. Accuracy of the results is satisfactory for values of integer and noninteger quantum numbers up to n= n'=60, n*= n'*<33 and for arbitrary values of screening constants of orbitals and internuclear distances.     

Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.     

Addition theorems for Slater-type orbitals in momentum space and their application to three-center overlap integrals

Using addition theorems for complete orthonormal sets of exponential type orbitals in the momentum representation introduced by the author, the addition theorems are established for Slater type orbitals in momentum space. With the help of these addition theorems, the general series expansion formulae in terms of the product of two-center overlap integrals are established for the three-center overlap integrals that arise in the solution of atomic and molecular problems occurring when explicitly correlated methods are employed. The formulae obtained for addition theorems and three-center overlap integrals are valid for arbitrary location and parameters of orbitals.     

Addition theorems for Slater-type orbitals and their application to multicenter multielectron integrals of central and noncentral interaction potentials

By the use of complete orthonormal sets of psi(alpha)-ETOs (alpha=1, 0, m1, m2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem (2hthN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals.     

One-range addition theorems for derivatives of Slater-type orbitals

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of -ETOs (Guseinov II (2003) J Mol Model 9:190–194), where =1, 0, –1, –2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree–Fock–Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron–nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.     

Effects of exposure time using preliminary concentrations on the mutagenic effect of the basic action of one-center and dual-center mutagens

The effect of exposition with pretreatment for thiophosphamide and dipin of human lymphocytes at Go phase was investigated. There were used 5 low concentrations of mutagens: 2, 0, 2; 2.10(-2); 2.10(-3), 2.10(-4) mcg/ml with different exposure: 1/4 hr, 1/2 hr, 1 hr and 4 hr and high concentration of 20 mcg/ml by which cell have been treated. There was discovered the dependence of the "protective" concentration on the exposition: the increase of exposition of pretreatment induced the decrease of "protective" concentration and vice versa.     

Analytical evaluation of Coulomb potential generated by multielectron molecule at arbitrary positions in space using one-range addition theorems of Slater type orbitals

By the use of unsymmetrical one-range addition theorems for Slater type orbitals (STO) and Coulomb potential introduced by the author, the analytical formulae in terms of two- and three-center nuclear attraction integrals, and linear combination coefficients of molecular orbitals are derived for the potential produced by the charges of molecule. These formulae can be useful for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the STO are used in the combined Hartree-Fock-Roothaan (HFR) theory suggested by the author. It should be noted that the symmetry of the potential obtained is the same as the symmetry of the molecule. As an example of application, the calculations have been performed for the potential produced by the ground state of BH ₃ molecule( ( 1a₁ )²( 2a₁ )²( 1e_x )²( 1e_y )²,¹A₁ ) \left( {{{\left( {1{a_1}} \right)}^2}{{\left( {2{a_1}} \right)}^2}{{\left( {1{e_x}} \right)}^2}{{\left( {1{e_y}} \right)}^2},{}^1{A_1}} \right) .     

Calculation of the diffusion coefficient of thiophene oligomers using molecular dynamics

Electropolymerisation is a very useful methodology for conducting polymers synthesis. A total comprehension of this process will help on the designing of new materials with improved optical and electrical properties. In this sense, computational simulations can deliver important information at atomic scale. Within a kinetic Monte Carlo scheme, diffusion rates are crucial to obtain accurate predictions; however, experimental values of this dynamic property for different oligomers are very scarce among literature. In this study, the diffusion coefficient (D) of thiophene oligomers (1Th–6Th) has been calculated using molecular dynamics simulations coupled with the Einstein expression. Results are in the order of experimental values, demonstrating that this methodology is a fast and reliable alternative to calculate diffusion coefficients with low computational costs.     

Calculation of static hyperpolarisabilities of donor-acceptor systems using a desktop molecular modelling package

A method for calculating the first static hyperpolarisability (₀) values of donor-acceptor molecules using a desktop molecular modelling package is presented. The ₀ values are deduced from a two-state model using geometries from AM1 and dipole moments from ZINDO/s calculations. The estimated ₀ values are in reasonable agreement with reported EFISH values. This method involves the use of a conventional PC and a molecular modelling package and does not require powerful workstations or long computational times.     

Mixing s orbitals into p and d orbitals. An attempt at bridging the angular overlap model and the valence shell electron pair repulsion model. Critique of the cellular ligand-field model

The stereochemistries of main group molecules have been discussed by using the angular overlap model in its molecular orbital oriented form (MO-AOM). Either ligand-field stabilisation of the ground state s²p^q−2 configuration, or s-p mixing, or both, provide a consistent bonding model for the stereochemistries. The transformation of the non-bonding orbitals into equivalent orbitals leads invariably to agreement with the lone-pair locations of the valence shell electron pair repulsion (VSEPR) model. The concepts of Hamiltonian-generated hybrids and pseudohemispherical molecular systems are found useful in this context. The MO-AOM formalism is also used for discussing s-d mixing in transition metal systems, and the energetic consequences within the ligand-field AOM (LF-AOM) are included. This is a second-order effect, which depends on squares and cross-products of radial parameters. It may still be quite large for tetragonal systems and for systems that deviate strongly from orthoaxiality. The usual ligand-additive property of the AOM is lost when the symmetry is lower than tetragonal and so is the energy separability into angular and radial factors. The cellular ligand-field model is found to be identical with the LF-AOM, except that its users consider it important not to acknowledge the formal hierarchy, MO-AOMLF-AOM, as relevant. The unintelligible concept of an active coordination void is found to be unnecessary and insufficient.     

A rapid and efficient method for site-directed mutagenesis using one-step overlap extension PCR.

A rapid method is described to efficiently perform site-directed mutagenesis based on overlap extension polymerase chain reaction (OE-PCR). Two template DNA molecules in different orientations relative to only one universal primer were amplified in parallel. By choosing a high dilution of mutagenic primers it was possible to run an overlap extension PCR in only one reaction without purification of intermediate products. This method which we have named one-step overlap extension PCR (OOE-PCR) can in principle be applied to every DNA fragment which can be cloned into a multiple cloning site of any common cloning vector.     

Calculation of NMR-relaxation parameters for flexible molecules from molecular dynamics simulations

Comparatively small molecules such as peptides can show a high internal mobility with transitions between several conformational minima and sometimes coupling between rotational and internal degrees of freedom. In those cases the interpretation of NMR relaxation data is difficult and the use of standard methods for structure determination is questionable. On the other hand, in the case of those system sizes, the timescale of both rotational and internal motions is accessible by molecular dynamics (MD) simulations using explicit solvent. Thus a comparison of distance averages (r ^–6–1/6 or r ^–31/3) over the MD trajectory with NOE (or ROE) derived distances is no longer necessary, the (back)calculation of the complete spectra becomes possible. In the present study we use two 200 ns trajectories of a heptapeptide of -amino acids in methanol at two different temperatures to obtain theoretical ROESY spectra by calculating the exact spectral densities for the interproton vectors and the full relaxation matrix. Those data are then compared with the experimental ones. This analysis permits to test some of the assumptions and approximations that generally have to be made to interpret NMR spectra, and to make a more reliable prediction of the conformational equilibrium that leads to the experimental spectrum.     

Calculation of excess free energy of molecular solids comprised of flexible molecules using Einstein molecule method

Knowledge of free energies of crystalline solid phases is pivotal in determination of phase equilibria; however, their computations using molecular simulations are quite challenging. In this paper, we apply the Einstein molecule method to compute the excess free energies of crystalline molecular solids comprising of molecules described by flexible models. This work can be viewed as an extension of the method described in Aragones et al. [J Chem Phys. 2013;139:a034104]. In this article, we present our calculations of the free energies of ice-Ih described by q-TIP4P/F model and Orcinol Form I described by the OPLS-AA forcefield. The free energies computed for ice-Ih are in agreement with previous reported results, and those of Orcinol are shown to be thermodynamically consistent. We demonstrate that the efficiency of our calculations compares favourably with existing methods. The method described here can be easily implemented in popular publicly available molecular dynamics packages without any modification to their existing source codes.     

Challenging AQP4 druggability for NMO-IgG antibody binding using molecular dynamics and molecular interaction fields

Neuromyelitis optica (NMO) is a multiple sclerosis-like immunopathology disease affecting optic nerves and the spinal cord. Its pathological hallmark is the deposition of a typical immunoglobulin, called NMO-IgG, against the water channel Aquaporin-4 (AQP4). Preventing NMO-IgG binding would represent a valuable molecular strategy for a focused NMO therapy. The recent observation that aspartate in position 69 (D69) is determinant for the formation of NMO-IgG epitopes prompted us to carry out intensive Molecular Dynamics (MD) studies on a number of single-point AQP4 mutants. Here, we report a domino effect originating from the point mutation at position 69: we find that the side chain of T62 is reoriented far from its expected position leaning on the lumen of the pore. More importantly, the strength of the H-bond interaction between L53 and T56, at the basis of the loop A, is substantially weakened. These events represent important pieces of a clear-cut mechanistic rationale behind the failure of the NMO-IgG binding, while the water channel function as well as the propensity to aggregate into OAPs remains unaltered. The molecular interaction fields (MIF)-based analysis of cavities complemented MD findings indicating a putative binding site comprising the same residues determining epitope reorganization. In this respect, docking studies unveiled an intriguing perspective to address the future design of small drug-like compounds against NMO. In agreement with recent experimental observations, the present study is the first computational attempt to elucidate NMO-IgG binding at the molecular level, as well as a first effort toward a less elusive AQP4 druggability.