Steric Energy Research Articles

Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.

Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are known. The experimental data of both channels are then used to verify and explain novel features of PNPF as compared with previous PNP models. The PNPF currents are in accord with the experimental I-V (V for applied voltages) data of the gramicidin A channel and I-C (C for bath concentrations) data of the calcium channel with 10(-8)-fold bath concentrations that pose severe challenges in theoretical simulations.

The effect of steric repulsion on the torsional potential of n-butane: a theoretical study

The origin of the rotational barriers in n-butane and gauche conformational energy, the prototypes of steric repulsion, has been re-examined by using energy decomposition analysis. The Pauli repulsion was found to be an important factor, but not the source of the barriers and gauche/anti energy difference. Rather, it should be considered as a driving force for structural changes accompanying the rotation. The repulsion (steric) energy partly transfers into the deformation energy of ethyl fragments and also affects a decrease in electrostatic, orbital and dispersion interactions by inducing the structural changes, particularly the central CC bond lengthening, while it becomes less destabilizing during the anti-butane rotation.

The origins of the directionality of noncovalent intermolecular interactions.

The recent σ-hole concept emphasizes the contribution of electrostatic attraction to noncovalent bonds, and implies that the electrostatic force has an angular dependency. Here a set of clusters, which includes hydrogen bonding, halogen bonding, chalcogen bonding, and pnicogen bonding systems, is investigated to probe the magnitude of covalency and its contribution to the directionality in noncovalent bonding. The study is based on the block-localized wavefunction (BLW) method that decomposes the binding energy into the steric and the charge transfer (CT) (hyperconjugation) contributions. One unique feature of the BLW method is its capability to derive optimal geometries with only steric effect taken into account, while excluding the CT interaction. The results reveal that the overall steric energy exhibits angular dependency notably in halogen bonding, chalcogen bonding, and pnicogen bonding systems. Turning on the CT interactions further shortens the intermolecular distances. This bond shortening enhances the Pauli repulsion, which in turn offsets the electrostatic attraction, such that in the final sum, the contribution of the steric effect to bonding is diminished, leaving the CT to dominate the binding energy. In several other systems particularly hydrogen bonding systems, the steric effect nevertheless still plays the major role whereas the CT interaction is minor. However, in all cases, the CT exhibits strong directionality, suggesting that the linearity or near linearity of noncovalent bonds is largely governed by the charge-transfer interaction whose magnitude determines the covalency in noncovalent bonds.

Quantum Chemical Studies of Anti-Prostatic Carcinoma DrugN-[4-cyano3-(trifluoromethyl)phenyl]-2-hydroxy-2-methyl-3-[(4methylphenyl)sulfonyl] Propanamide (bicalutamide)

N-[4-cyano-3-(trifluoromethyl)phenyl]-2-hydroxy-2-methyl-3-[(4-methylphenyl)sulfonyl]propanamide (bicalutamide) is an oral medication that is used for treating cancer of the prostate. It belongs to a class of drugs called anti-androgens. Quantum chemical studies of bicalutamide were based on Arguslab software. The steric energy was evaluated in terms of potential energy as a sum of energies associated with bonded interactions (bond length, bond angle and dihedral angle) as well as non-bonded interactions (van der Waals and electrostatic). Surfaces were created to visualize excited state properties such as highest occupied molecular orbital's, lowest unoccupied molecular orbital's and electrostatic potential (ESP) mapped density. The steric energy for bicalutamide was calculated to be 0.963933 a.u. (604.877867 kcal/mol). The most energetically favourable conformation of bicalutamide was found to have a heat of formation of 7696.375900 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using RHF/PM3 method in ArgusLab software. The most feasible position for bicalutamide to block androgen receptors on the cells of tissues was found to be-189.888176 au (−119156.737100 Kcal/mole).

Molecular Mechanics Geometry Optimization and Excited-State properties of Cardioprotective Drug 4, 4′-(2S)-Propane-1, 2Diyldipiperazine-2, 6-Dione (Dexrazoxane)

Dexrazoxane (4, 4′-(2S)-propane-1, 2-diyldipiperazine-2, 6-dione) a cyclic derivative of edetic acid, is a sitespecific cardioprotective agent that effectively protects against anthracycline-induced cardiac toxicity. Geometry optimization was performed using Arguslab software. The atomic coordinates, bond length, bond angles, dihedral angles, Muliken atomic charges, ZDO atomic charges and final steric energy evaluation of dexrazoxane were calculated. The highest occupied molecular orbitals, lowest unoccupied molecular orbital, electron clouds, and electrostatic potential mapped density surfaces were created. Heat of Formation of dexrazoxane was 622.179600 kcal/mol. The steric energy calculated for dexrazoxane was 0.026350 a.u. (16.535264 kcal/mol). SCF energy was found to be-129.162975 au (−81051.064000 kcal/mol) as calculated by RHF/AM1 method, performed by Argusl ab 4.0.1 suite. The SCF energy represents the most feasible energy where dexrazoxane would bind to the receptor for effective protection against anthracycline-induced cardiac toxicity.

Computer-aided drug design of an anti-angiogenic and immunomodulatory agent, -(2,4-dioxocyclohexyl)-1H-isoindole-1,3(2H)-dione (thalidomide)

2-(2,4-dioxocyclohexyl)-1H-isoindole-1,3(2H)-dione (thalidomide) is an oral agent with anti-angiogenic and immunomodulatory properties. Computational geometry optimization was performed to determine the steric energy, heat of formation and self-consistent field(SCF) energy of thalidomide. The molecular mechanics potential energy function wer evaluated in terms of energies associated with bonded interactions (bond length, bond angle and dihedral angle) as well as non-bonded interactions (Vander Waals and electrostatic). Surfaces were created to visualize excited state properties such as highest occupied molecular orbital's, lowest unoccupied molecular orbital's and electrostatic potential (ESP) mapped density. Heat of Formation of thalidomide was 655.2578 kcal/mol, the steric energy calculated for thalidomide was 0.10063593 a.u. (63.150058kcal/mol) and SCF energy was found to be-119.890047 au (−75232.2088 00kcal/mol) as calculated by RHF/MNDO method using Arguslab 4.0.1 suite. The most feasible position for thalidomide to act as an anti-angiogenic and immunomodulatory agent, was found to be-119.890047 au (−75232.208800 kcal/mol)

Theoretical exploration of the nanoscale host-guest interactions between [n]cycloparaphenylenes (n = 10, 8 and 9) and fullerene C₆₀: from single- to three-potential well.

The nanoscale host-guest interactions between [n]cycloparaphenylene ([n]CPP; n = 10, 8 and 9) nano-ring and fullerene C60 were explored theoretically. It is found that relatively small variations in the sizes of the [n]CPP host lead to very significant changes in encapsulation property toward the fullerene C60 guest. Expectedly, one stable inclusion-configuration of [10]CPP⊃C60 and one floating-configuration of [8]CPP⊃C60 are located on the potential surfaces of the two complexes, respectively. Unexpectedly, besides a floating-configuration (F-[9]CPP⊃C60), another stable inclusion-configuration (I-[9]CPP⊃C60) is also located on the potential surface of [9]CPP⊃C60 host-guest complex. Interaction energies and natural steric analysis show that these complexes are stabilized by balancing concave-convex π-π attractive and steric repulsive host-guest interactions. In contrast, the steric repulsive energy (Es) between host and guest of I-[9]CPP⊃C60 is as high as 233.12 kJ mol(-1), which is much larger than those in other complexes. The movements of C60 guest through the cavities of [n]CPP host (n = 10, 8 and 9) are simulated by calculating the energy profile, and the results interestingly reveal that the encapsulation of C60 by [10]CPP is in the manner of a single-potential well, by [8]CPP in the manner of a double-potential well, and by [9]CPP in the special manner of a three-potential well. We predict that the movement of C60 guest through the cavity of [9]CPP host should be experimentally observable owing to the relatively low energy barrier (<50 kJ mol(-1), M06-2X/6-31G(d)). Charge population analysis shows that an obvious charge transfer between host and guest takes place during the formation of I-[9]CPP⊃C60, which is different from those during the formation of [8]CPP⊃C60, [10]CPP⊃C60 and F-[9]CPP⊃C60. Additionally, the host-guest interaction regions were detected and visualized in real space based on the electron density and reduced density gradient.

The conformation of acetaldehyde: a simple molecule, a complex explanation?

Consider acetaldehyde (ethanal for progressive nomenclaturists). What conformation does it adopt, and why? This question was posed of me by a student at the end of a recent lecture of mine. Surely, an easy answer to give? Read on … There really are only two possibilities, the syn and anti. Well, I have discovered it is useful to start with a search of the Cambridge data base. With R=H or C, X unspecified, acyclic and T ≤ 175K, two searches were performed. The first identified the torsion around O=C-C-H. This clearly shows a maximum at 120° (with twice the probability), and a smaller one at 0°. This matches syn; the anti conformation above would be expected to have peaks at 60° and 180°; the latter in particular is singularly missing. An alternative search is to define the distance between the oxygen and the H. For the syn conformer, distances of ~2.5 and 3.1Å are expected; for the anti conformer, 2.7 and 3.3Å. Again, syn matches better. Remember, searches based on the position of a hydrogen are less reliable than most, so these distributions provide only a statistical indication. Now for a (ωB97XD/6-311G(d,p) calculation of the rotational barrier. The minima occur at torsions of 0, 120 and 240°, matching syn, although the barrier is very low. Now to try to find explanations. The standard one finds this in three effects: Donation from two C-H bonds (R=H above) into the π*C=O NBO orbital (in the manner that was used to explain the cis-orientation of the two methyl groups in cis-butene). Donation from the single co-planar C-H bond into the σ*C=O NBO orbital (blue bonds above) Pauli bond-bond repulsions between two filled NBOs. Effect 1 has an NBO perturbation energy E(2) of 7.0 kcal/mol for the syn conformer and 6.45 for the anti. The explanation is the π*C=O NBO “leans outward”, overlapping better with the C-H bonds in the syn than in the anti. the One up to the syn! Effect 2 has values of 1.3 for the syn and 4.1 for the anti. The latter now has the edge. But wait, there are other (smaller) interactions. The syn has an antiperiplanar orientation of the two C-H bonds shown above (X=H,red), E(2) = 3.3 vs 0.6 for the corresponding syn-planar orientation in the anti-conformation. It’s now a tie; neck-and-neck. Effect three suggests that the disjoint NLMO steric exchange energy is 54.34 for the anti and 53.88 (i.e. lower) for the syn. It is vaguely disappointing that no absolutely clear-cut explanation emerges. But then the difference (in total free energy) is only 1.4 kcal/mol. But even this small difference in energy can manifest in fairly clear-cut conformational preferences obtained from crystal structures. Ultimately of course, all effects in chemistry are reducible to the sum of lots of small effects (in other words unpredictable until one does the sum). I cannot end without mentioning the largest of all the NBO interactions, namely the in-plane lone pair on the oxygen as donor and the aldehyde proton C-H as acceptor (X=H). This has values of 29.3 for syn and 28.8 kcal/mol for anti. This manifest (inter alia) in a greatly reduced C-H vibrational wavenumber (ν 2982 for syn, 2900 cm-1 for anti) compared to the methyl C-H values (~3043-3164). So this tiny little molecule ended up a little less obvious than might have seemed at the outset. One can find interesting things in even the tiniest of things! HC…C-H alignment. Click for 3D. O=C*…C-H alignment. Click for 3D.

In Silico Geometry Optimization, Excited-State Properties of (2E)-N-Hydroxy-3-[3-(Phenylsulfamoyl) Phenyl] prop-2-Enamide (Belinostat) and its Molecular Docking Studies with Ebola Virus Glycoprotein

The histone deacetylase inhibitor (2E)-N-hydroxy-3-[3-(phenylsulfamoyl)phenyl]prop-2-enamide (belinostat) is a drug designed for the treatment of hematological malignancies and solid tumors. Geometry optimization of (2E)-N-hydroxy-3-[3-(phenylsulfamoyl)phenyl]prop-2-enamide (belinostat) using Argus lab software was performed. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles. The excited states of belinostat were created. The final self-consistent field (SCF) energy was found to be be 126.3659168682 au (−79295.8815 kcal/mol). This is the average interaction between a given belinostat particle and other belinostat particles of a quantum-mechanical system consisting of many particles. The most energetically favourable conformation of belinostat was found to have a heat of formation of 581.1137 kcal/mol via PM3 (NDDO) RHF SCF Type. The steric energy calculated for belinostat was 0.64665673 a.u.(405.78359283 kcal/mol). Molecular docking result revealed the binding free energy. The global binding energy value-28.87 Kcal/mole was ranked first because it had the least energy. The most feasible position for belinostat to inhibit ebola virus glycoprotein was predicted to be-28.87 kcal/mol.

Conformational Analysis of Chemically Reactive Groups in Polikon K. Part 1

A preliminary conformational analysis of chemical reactions of functional groups in Polikon K was performed. Five mechanisms for chemical reactions of polyacrylonitrile fibers with amines were identified. The level of steric energy was estimated preliminarily as a characteristic of the heterostructure strain. A general scheme for calculating the potential energy of the Polikon K molecular system was based on Allinger force field concepts.

Conformational analysis and excited-state properties of a highly potent and totally selective aromatase inhibitor, 4, 4′-(1H-1, 2, 4-triazol-1-ylmethanediyl) dibenzo nitrile (letrozole)

4, 4′-(1H-1, 2, 4-triazol-1-ylmethanediyl)dibenzonitrile (letrozole) is a highly potent and totally selective aromatase inhibitor used in treatment of early breast cancer in women who have experienced menopause (end of monthly menstrual periods) and who have had other treatments, such as radiation or surgery to remove the tumor. Conformational analysis studies of letrozole were based on Arguslab software. The molecular mechanics potential energy function wer evaluated in terms of energies associated with bonded interactions (bond length, bond angle and dihedral angle) as well as non-bonded interactions (Vander Waals and electrostatic). Surfaces were created to visualize excited state properties such as highest occupied molecular orbital's, lowest unoccupied molecular orbital's and electrostatic potential (ESP) mapped density. The steric energy for letrozole was calculated to be 0.116739 a.u. (73.255075 kcal/mol). The most energetically favourable conformation of letrozole was found to have a heat of formation of 1208.5864 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using RHF/AM1 method with a net charge of-1 and valence electron of 94, in ArgusLab software. The most feasible position for letrozole to act as a highly potent and totally selective aromatase inhibitor was found to be-116.271466 au (−72961.512600 kcal/mol)

Quantum Chemical Studies of Anti-Cancer Chemotherapy Drug 4-Amino1-[(2R, 3R, 4S, 5S)-3, 4, 5-Trihydroxytetrahydrofuran-2-yl]-1, 3, 5-Triazin2(1H)-one (Azacitidine)

4-amino-1-[(2R, 3R, 4S, 5S)-3, 4, 5-trihydroxytetrahydrofuran-2-yl]-1, 3, 5-triazin-2(1H)-one (azacitidine) is an anticancer chemotherapy drug mainly used in the treatment of myelodysplastic syndrome (MDS). Azacitidine is a chemical analogue of the cytosine, a nucleoside found in DNA and RNA. Conformational analysis and geometry optimization of azacitidine was performed according to the Hartree-Fock (HF) calculation method by Argus Lab 4.0.1 software. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles, torsional effects of twisting about single bonds, the Vander Waals attractions or repulsions of atoms that came close together, and the electrostatic interactions between partial charges azacitidine due to polar bonds. Surface created to visualize ground state properties as well as excited state properties such as orbital, electron densities, electrostatic potential (ESP) spin densities. The generated grid data were used to make molecular orbital surface, visualized the molecular orbital, electrostatic potential map and electron density surface. The steric energy for azacitidine was calculated to be 0.12162642 a.u.(76.32179805 kcal/mol). It was concluded that the lowest energy and most stable conformation of azacitidine was 0.12162642 a.u.(76.32179805 kcal/mol) The most energetically favourable conformation of azacitidine was found to have a heat of formation of 157.6452 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using RHF/PM3 method in ArgusLab software. The most feasible position for azacitidine to induce antineoplastic activity in the receptor was found to be-110.6126839099 au (−69410.5697 kcal/mol)

Conformation Analysis and Self-Consistent Field Energy of Immune Response Modifier, 1-(2-methylpropyl)-1H-imidazo[4, 5]quinolin-4-amine (Imiquimod)

1-(2-methylpropyl)-1H-imidazo[4, 5]quinolin-4-amine (imiquimod) is an immune response modifier and is used to treat genital warts, superficial basal cell carcinoma, and actinic keratosis. Conformational analysis and geometry optimization of imiquimiod was performed according to the Hartree-Fock (HF) calculation method by Argus Lab 4.0.1 software. Molecular mechanics calculations were based on specific interactions within the molecule. These interactions included stretching or compressing of bond beyond their equilibrium lengths and angles, torsional effects of twisting about single bonds, the Van der Waals attractions or repulsions of atoms that came close together, and the electrostatic interactions between partial charges in imiquimod due to polar bonds. The steric energy for imiquimiod was calculated to be 59.09 kcal/mol. It was concluded that the lowest energy and most stable conformation of imiquimiod was 59.09 kcal/mol. The most energetically favourable conformation of imiquimiod was found to have a heat of formation of 908.38 kcal/mol. The self-consistent field (SCF) energy was calculated by geometry convergence function using Argus Lab software. The most feasible position for the drug to interact with the receptor was found to be-95.99 au (−60240.26 kcal/mol).

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels.

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part of the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form - called Gibbs-Fermi entropy - that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10(8)-fold range of Ca(2+) concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms ranging from binding, to permeation, blocking, flexibility, and charge/space competition of the channel.

Structure-biological function relationship extended to mitotic arrest-deficient 2-like protein Mad2 native and mutants-new opportunity for genetic disorder control.

Overexpression of mitotic arrest-deficient proteins Mad1 and Mad2, two components of spindle assembly checkpoint, is a risk factor for chromosomal instability (CIN) and a trigger of many genetic disorders. Mad2 transition from inactive open (O-Mad2) to active closed (C-Mad2) conformations or Mad2 binding to specific partners (cell-division cycle protein 20 (Cdc20) or Mad1) were targets of previous pharmacogenomics studies. Here, Mad2 binding to Cdc20 and the interconversion rate from open to closed Mad2 were predicted and the molecular features with a critical contribution to these processes were determined by extending the quantitative structure-activity relationship (QSAR) method to large-size proteins such as Mad2. QSAR models were built based on available published data on 23 Mad2 mutants inducing CIN-related functional changes. The most relevant descriptors identified for predicting Mad2 native and mutants action mechanism and their involvement in genetic disorders are the steric (van der Waals area and solvent accessible area and their subdivided) and energetic van der Waals energy descriptors. The reliability of our QSAR models is indicated by significant values of statistical coefficients: Cross-validated correlation q2 (0.53–0.65) and fitted correlation r2 (0.82–0.90). Moreover, based on established QSAR equations, we rationally design and analyze nine de novo Mad2 mutants as possible promoters of CIN.

Correlations between hardness, electronegativity, anomeric effect associated with electron delocalizations and electrostatic interactions in 1,4,5,8-tetraoxadecalin and its analogs containing S and Se atoms

Hybrid density functional theory (B3LYP/6-311++G∗∗) based method and natural bond orbital (NBO) interpretation were used to investigate the correlations between the global hardness (η), global electronegativity (χ), anomeric effect associated with electron delocalization and electrostatic model associated with dipole–dipole interactions (four important conceptual descriptor in chemistry and physics) in 1,4,5,8-tetraoxadecalin (1), 1,4,5,8-tetrathiadecalin (2) and 1,4,5,8-tetraselenadecalin (3). B3LYP/6-311++G∗∗ results showed that the calculated Gibbs free energy and corrected electronic energy differences between the cis- and trans-stereoisomers [i.e. ΔG=Gtrans−Gcis, ΔEo=Eo(trans)−Eo(cis)] decrease from compound 1 to compound 3. On the other hand, the global hardness (η) differences between the cis- and trans-stereoisomers (i.e. Δ[η(cis)−η(trans)]) decrease from compound 1 to compound 2 but increase from compound 2 to compound 3. Accordingly, the variation of ΔG=Gtrans−Gcis, ΔEo=Eo(trans)−Eo(cis) parameters from compound 1 to compound 3 cannot be justified by the variation of their corresponding global hardness. Therefore, compounds 2 and 3 do not obey the maximum hardness principle. Interestingly, the calculated global electronegativity (χ) differences between the cis- and trans-stereoisomers (i.e. Δ[χ(cis)−χ(trans)]) decrease from compound 1 to compound 3. NBO results showed that the anomeric effect associated with the electron delocalization is in favor of the cis stereoisomers. Effectively, with the decrease of the anomeric effect, ΔG=Gtrans−Gcis, ΔEo=Eo(trans)−Eo(cis) parameters decrease from compound 1 to compound 3. Therefore, the variations of the anomeric effect and global electronegativity explain the variations of ΔG=Gtrans−Gcis, ΔEo=Eo(trans)−Eo(cis) parameters from compound 1 to compound 3. It should be noted that the variation of the calculated dipole moment differences between the cis and trans stereoisomers [i.e. Δ(μ(cis)−μ(trans)] does not justify the variation of ΔG=Gtrans−Gcis, ΔEo=Eo(trans)−Eo(cis) parameters from compound 1 to compound 3. The total steric exchange energy differences between the cis- and trans-stereoisomers (Δ[TSEEcis−TSEEtrans]) increase from compound 1 to compound 3 which in the trend observed for the anomeric effect and global electronegativity. The correlations between the global hardness, global electronegativity, anomeric effect, zero point energies, electrostatic model, structural parameters, corrected electronic energies (ΔEo), and thermodynamic parameters [ΔH, ΔG and ΔS] of compounds 1–3 have been investigated.

Analytical models of calcium binding in a calcium channel.

The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na(+) and Ca(2+) for [CaCl2] ranging from 10(-8) to 10(-2) M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation-that includes both steric and correlation effects-is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.

Multiscale Analysis Approach to Find the Dynamic Characteristics of Graphene Sheet

The research work addresses question on dynamic characteristic of structure which exhibit periodicity at nanoscale viz. single layer graphene sheet using multiscale analysis approach. The carbon-carbon bond of graphene sheet is modeled as space frame element whereas the carbon atom is modeled as 3D-mass element without rotary inertia. Molecular structural mechanics (MSM) model has been used to find the equivalent geometric and elastic properties of space frame element to represent carbon-carbon bond. In molecular structural mechanics model, force field is expressed in the form of steric potential energy by omitting the electrostatic interaction. Sectional stiffness parameters are linked with the force field constants to derive the equivalent elastic and geometric properties of space frame element. This approach is used here to investigate the dynamic behavior of single layer graphene sheet. Simulations have been carried out with different values of aspect ratio to know the effect of variation in length and width on the natural frequencies of graphene structure. Molecular dynamic simulation has also been carried out on the same structure of graphene sheet to validate the results of proposed molecular structural mechanics model.

DFT-steric-based energy decomposition analysis of intermolecular interactions

Application of a novel energy decomposition analysis (EDA) based on the recently introduced density functional theory (DFT) steric analysis is presented. The method is compared with results from the constrained space orbital variations (CSOV) and Bader’s quantum theory of atoms in molecules (QTAIM) topological analysis. These two analyses explain the driving forces for the formation of dimers from different perspectives. The components of the DFT steric analysis are shown to have good linear relationships with the total interaction energy for hydrogen-bonding dimers. It is observed that some components from the new EDA method, such as steric energy, favor the formation of dimers. Moreover, comparison of the different contributions between CSOV and the DFT steric analysis provides additional insights into the physical meaning of the respective components. In addition to the total interaction energy, DFT steric energy has been found to correlate with the electron density at critical points from QTAIM analysis in different patterns for different molecular systems, which qualitatively accounts for the linear relationships between the steric and total interaction energy. The DFT steric energy is found to represent effects arising from the spatial arrangement of the electron density when dimers form, reminiscent of the steric effects invoked in chemical systems.

Exploring the role of steric effect in the stability of clusters: Water hexamer as a test case

Steric effect is one of the most widely used concepts in chemistry and has long been known to play imperative roles in various phenomena. In this paper, on the basis of a quantitative description of steric effect, which is based on a new energy partition scheme where the total electronic energy is decomposed into contributions from three independent effects of steric, electrostatic, and the Fermionic quantum, the steric effects in different conformers of water hexamer have been investigated. It is shown that the steric repulsion has a strong effect on conformations stability. Reasonable correlations between relative electronic energies and steric energies are revealed. We find that more stable structures of water hexamer prefer to have smaller size and less steric repulsion.