Semi-empirical Potential Functions Research Articles

Optimal sequence selection in proteins of known structure by simulated evolution.

Rational design of protein structure requires the identification of optimal sequences to carry out a particular function within a given backbone structure. A general solution to this problem requires that a potential function describing the energy of the system as a function of its atomic coordinates be minimized simultaneously over all available sequences and their three-dimensional atomic configurations. Here we present a method that explicitly minimizes a semiempirical potential function simultaneously in these two spaces, using a simulated annealing approach. The method takes the fixed three-dimensional coordinates of a protein backbone and stochastically generates possible sequences through the introduction of random mutations. The corresponding three-dimensional coordinates are constructed for each sequence by "redecorating" the backbone coordinates of the original structure with the corresponding side chains. These are then allowed to vary in their structure by random rotations around free torsional angles to generate a stochastic walk in configurational space. We have named this method protein simulated evolution, because, in loose analogy with natural selection, it randomly selects for allowed solutions in the sequence of a protein subject to the "selective pressure" of a potential function. Energies predicted by this method for sequences of a small group of residues in the hydrophobic core of the phage lambda cI repressor correlate well with experimentally determined biological activities. This "genetic selection by computer" approach has potential applications in protein engineering, rational protein design, and structure-based drug discovery.

Configuration‐dependent properties of polyoxyethylene chains in the third‐order interaction approximation

AbstractConformational energies of polyoxyethylene chains in the third‐order interaction approximation are calculated using a semiempirical potential energy function in the usual manner. Configuration‐dependent properties of POE in the third‐order are also calculated, and more close to the experimental data.

Diffusion of xenon on a platinum surface: the influence of correlated flights

Xenon diffusion on a Pt(111) surface is modeled using a classical trajectory simulation employing an accurate semi-empirical potential function. Good agreement with experimental results suggests that this system may provide a good empirical test for Hamiltonian transport models. Analysis of the trajectory data indicates that long and correlated flights are centrally important in the diffusion process, although anomalous diffusion is not observed. Evidence is seen for the influence of low order periodic orbits in promoting long flights.

A new semiempirical potential function for hydrogen bonds and its possible use in studying the DNA molecule

Abstract A semiempirical potential function V ( r,R ) is proposed for describing the protons in hydrogen bonds. It consists of: the Morse potential V A ( r ), which describes the covalent bond AH in the R 1 AH⋯BR 2 system; a Coulombic term E e.s. , which contains the Coulombic point interaction of each atom of the R 1 AH group with the BR 2 molecule and the interaction of the hydrogen atom with the R 1 A group having non-equilibrium lengths R  R 0 ; the potential V R ( R ), which describes the exponential repulsion of atoms A and B owing to the partial overlap of their shells; another Morse potential V B ( R—r ), which accounts for all other effects such as the redistribution of charge density by the approach of the hydrogen and boron atoms, their mutual polarization, and partly also Van der Waals forces. The parameters of the proton potential were found for the (H 2 O) 2 dimer and for three hydrogen bonds of a guanine—cytosine (GC) pair for weak and medium strong hydrogen bonds without high proton excitation levels. Using the dependence on R of the bond energy ϵ( R ) (for the water dimer) and the V ( r,R ) values at R = R 0 (for the GC pair), we extrapolated the V ( r,R ) functions to non-equilibrium r = R 0 and R = R 0 values. A simple method of solving a one-dimensional Schrodinger equation is proposed for such a potential function. Wavefunctions and the corresponding energy levels were obtained. These data make it possible to study the influence of hydrogen bonds in the ground and excited states on the character of the atomic vibrations in the GC pair and the processes in poly-GC with one adenine-thymine pair by absorption of excess energy and also the influence of dielectric surroundings (in particular, water) on the properties of the hydrogen bonds in (H 2 O) 2 .

Comparison of semi-empirical potential functions for silicon and germanium.

We report the results of investigations into the behavior of the crystalline and liquid phases of silicon and germanium as they are modeled by the Tersoff and modified-embedded-atom-method (MEAM) potentials. The structure of the solid-liquid interface produced by each potential is determined, as are the melting points corresponding to each potential model. The equilibrium properties of both crystalline and liquid silicon and germanium as modeled by the Tersoff and MEAM potentials are then presented. The Tersoff potential is found to overestimate greatly the melting point of both silicon and germanium, while the MEAM underestimates the melting point of silicon by approximately 15%. The MEAM does not yield a stable liquid phase of germanium. Both potential models produce a (100) solid-liquid interface for both semiconductors that is rough, while the (111) interface is found to be atomically smooth. The Tersoff potential yields an amorphous phase for both silicon and germanium, but efforts to produce an amorphous MEAM phase were unsuccessful. Rapid solidification of MEAM silicon produced unphysical regrowth velocities.

Fundamental aspects of film nucleation and growth in chemical vapor deposition

The importance of surface reconstruction plus the generation of stress and electric fields at expanding islands during film formation are extremely important considerations for both surface cluster formation and ledge movement kinetics in the overall film deposition process. Using computer simulations and semi-empirical potential energy functions for Si and GaAs, both long-range field effects and cluster excess energy effects are demonstrated. Using a continuum approach with a ledge energy that depends on cluster radius, great differences relative to the classical nucleation picture are found. For vicinal surface orientations, an equation for film growth velocity is developed which incorporates gas phase transport, surface transport, ledge collection efficiency, ledge attachment kinetics and excess energy storage due to deposition stress and adsorbate trapping. The paper first treats the case of Si film formation from SiH 4 in H 2 with only SiH 2 forming in the adlayer. It then extends the treatment to deal with other Si intermediates formed in the adlayer which then desorb into the gas phase. Finally, the treatment is extended to consider SiN x film formation from SiH 4 + NH 3 in H 2.

Adatom processes near step-edges and evolution of long range order in semiconductor alloys grown from vapor phase

Single and multiple adatom energetics near the [110] and [1̄10] step edges on the As (2×4) reconstructed (missing dimer) GaAs (001) surface are examined to shed light on the issue of the occurrence of long range order in III-III-V alloys. Semiempirical potential functions and the simulated annealing procedure are employed. Step-induced local breaking of symmetry and the adatom-ledge interaction are found to favor the evolution of the 〈111〉 CuPt-B type of ordering.

The role of ledges in stress tensor-mediated surface processes for Si and GaAs

Calculation results of terrace and ledge reconstruction-induced surface stress tensors, using semiempirical potential energy functions for Si, GaAs, GaAs/Al, and GaAs/Si, are reviewed. Long-range (∼50 to 100 A) interaction effects between ledges and between interfaces are pre sented. Two-dimensional homogeneous and heterogeneous nucleation effects are also presented, showing that Actatom cluster populations are strongly influenced by these reconstruction events. The consequences of these reconstruction-induced surface fields on γ plots, ledge motion kinetic laws, surface Actatom transport, and solute partitioning at ledges are discussed. The numerical results were generated largelyvia Monte Carlo calculations and thus neglect entropy effects.

Fundamental aspects of film nucleation and growth

At real surfaces, atomic reconstruction generates a surface stress tensor that influences all subsequent surfaces processes like roughening, cluster formation, nucleation, adsorption layer characteristics, and layer flow kinetics. Here, computer simulation results using semiempirical potential energy functions for the Si–Ga–As and Al–Ga–As systems are used to illustrate some important long-range effects on ledge/ledge interaction and cluster excess energy that would not have been anticipated using the conventional dangling bond viewpoint. New insight has also been added to adsorption layer isotherm considerations and an equation for crystal growth velocity, which incorporates gas phase transport, surface transport, ledge attachment kinetics, plus ledge trapping of adsorbate species, is given.

Structural studies of analgesics and their interactions. XII. Structure and interactions of anti-inflammatory fenamates. A concerted crystallographic and theoretical conformational study.

A theoretical conformational analysis of fenamates, which are N-arylated derivatives of anthranilic acid or 2-aminonicotinic acid with different substituents on the aryl (phenyl) group, is reported. The analysis of these analgesics, which are believed to act through the inhibition of prostaglandin biosynthesis, was carried out using semi-empirical potential functions. The results and available crystallographic observations have been critically examined in terms of their relevance to drug action. Crystallographic studies of these drugs and their complexes have revealed that the fenamate molecules share a striking invariant feature, namely, the six-membered ring bearing the carboxyl group is coplanar with the carboxyl group and the bridging imino group, the coplanarity being stabilized by resonance interactions and an internal hydrogen bond between the imino and carboxyl groups. The results of the theoretical analysis provide a conformational rationale for the observed invariant coplanarity. The second six-membered ring, which provides hydrophobicity in a substantial part of the molecule, has limited conformational flexibility in meclofenamic, mefenamic and flufenamic acids. Comparison of the conformational energy maps of these acids shows that they could all assume the same conformation when bound to the relevant enzyme. The present study provides a structural explanation for the difference in the activity of niflumic acid, which can assume a conformation in which the whole molecule is nearly planar. The main role of the carboxyl group appears to be to provide a site for intermolecular interactions in addition to helping in stabilizing the invariant coplanar feature and providing hydrophilicity at one end of the molecule. The fenamates thus provide a good example of conformation-dependent molecular asymmetry.

Simulation of GaAs cluster formation on GaAs(001̄), AlAs(001̄), Si(001), and As1/Si(001) surfaces

Recently developed semiempirical potential energy functions for the Ga–As–Si and Ga–As–Al systems have been applied here to determine the excess formation energy for GaAs clusters on GaAs(001̄), AlAs(001̄), Si(001), and one atomic layer As-covered Si(001) substrates as a function of cluster size and cluster shape by the Monte Carlo technique. Pyramidal type ledges on the GaAs clusters are found to be the favored ledge for the first three layers while an inverted-pyramidal type ledge is also favored in certain cases for the As1/Si(001) substrate. Cluster formation at ledges is compared with cluster formation on a flat terrace for the Si(001) and the As1/Si(001) substrates.

Conformational studies of N‐acetyl‐N′‐methylamide derivatives of α‐aminobutyric acid, norvaline, and valine. II. Conformational energy calculations and comparison with experimental results

AbstractConformational analyses on a series of dipeptides CH3—C*O—NH—CH(R)—C*O—HN—CH3 with side chains such as R = CH2CH3, CH2CH2CH3, and CH(CH3)2 are described. Calculations were carried out by using semiempirical potential energy functions of Brant et al. The results were compared with those reported by Vásquez et al. and Chuman et al., who employed the ECEPP program in their analyses. The averages of the vicinal coupling constant J and the side‐chain conformer fractions p(χ1) and p(χ2)′ were estimated therefrom for preferred conformations. The characteristic features of the experimental observations derived from the 1H‐nmr measurements are reasonably well reproduced by these calculations.

Theoretical studies on alpha-helix--DNA interactions.

The interaction energies between (Ala)10 and alpha-helix fragment and different nucleotide sequences in right-handed B-form have been optimized using semi-empirical potential energy functions. The energies are calculated for two different orientations of the alpha-helix, viz., when the alpha-helix axis taken in the N----C direction is (i) parallel and (ii) antiparallel to the 5'-3' ascending strand of DNA, proximal to it. When both the DNA molecule as well as the alpha-helix are treated as rigid molecules it is found that a polyalanine alpha-helix has slightly more favourable contacts when it is in the proximity of a four nucleotide sequence of 5'-(N-A-T-N)-3' type, where N is either a purine or a pyrimidine. However, when the two interacting molecules are allowed to undergo local structural variations then the interaction energy appears to be independent of the base sequence confirming the non-specific nature of these interactions.

Computer simulation of ledge formation and ledge interaction for the silicon (111) free surface

Both strip and triangular clusters, composed of <2 11 > ledges, have been simulated on the Si (111) surface. The long range ledge-ledge interaction and the surface stress tensor distribution have been evaluated for these two pill-box geometries using a semi-empirical potential energy function that incorporates both two-body and three-body contributions. The consequences of the ledge-ledge interaction on two-dimensional nucleation for Si (111) has been evaluated as a function of Si adatom supersaturation and shown to differ significantly from conventional theory where such interaction is neglected.

Free surfaces and multilayer interfaces in the GaAs/AlAs system

Semiempirical potential energy functions have been utilized for a variety of calculations in the Ga-Al-As system: (1) surface energies have been calculated for several orientations of GaAs; (2) ledge energies for the GaAs(00 1 ) (As terminated) surface show long range interaction effects with the ledge energy increasing with spacing; (3) GaAs(001)/AlAs(001) superlattices have been simulated for a range of interlayer spacings with the excess interfacial energy per interlayer increasing from 5 erg/cm 2 at an interlayer spacing of 1 molecular layer (5.8 Å) to 50 erg/cm 2 at an interlayer spacing of 18 molecular layers (103.8 Å).

Computer simulation of thin amorphous Si films on crystalline Si substrates

Using a semiempirical potential energy function for Si, thin amorphous films of Si have been simulated on crystalline Si by a partial melting and subsequent quenching process. After relaxation at 450 K., the dominant structural feature was a dense free surface skin with a void layer underneath for both c-Si(100) and c-Si(111) substrates and for film thicknesses up to 16 A. Tetrahedral coordination was maintained throughout the amorphous region and structural differences were noted in the α-Si/c-Si interface region for the two orientations considered.

Long-range ledge-ledge interactions on Si(111) surfaces: I. No kinks or surface point defects

Surface ledges of the [211̄] and [2̄11] type on the Si(111) surface provide a dilational contribution to the strongly compressive surface stress tensor. Computer calculations using a semiempirical potential energy function show (a) monatomic ledge-ledge interaction even at spacings of 50 Å, (b) strong reconstruction on some ledge orientations and negligible changes on others leading to ledge energies in the range 0.01–0.22 eV/atom compared to a face energy of 0.38 eV/atom, and (c) that the surface stress tensor dominates the relaxation around ledges.

An empirical potential function for cyclopropene and vibrational spectra of cyclopropene-1,3-d2

A potential function has been fitted to the vibrational fundamentals of eight of the nine possible hydrogen-deuterium isotopomers of cyclopropene. For one of these species, the 1,3-d/sub 2/molecule, infrared and Raman spectra are reported for the first time and assigned. The fundamental frequencies (in cm/sup -1/) of the 1,3-d/sub 2/ species are 3134, 2972, 2384, 2203, 1598, 1348, 1104, 1020, 979, 903, (821), 771, 749, 657, and 475. The value in parentheses is in doubt. The new empirical potential function is a significant improvement over the earlier one of Wiberg and Wendoloski, which came from fitting only the frequencies of the four isotopomers of C/sub 2v/ symmetry. The empirical potential function is discussed in relationship to the later semiempirical potential function of Wiberg, Dempsey, and Wendoloski, which was obtained by fitting the diagonal force constants to observed frequencies while using scaled, ab initio values of the off-diagonal force constants. Accurate frequencies are predicted for the as-yet unknown 1,2,3-d/sub 3/ isotopic species.

Surface Stress Tensor Mediation of the Ledge Nucleation/Growth Process with the Surface Reconstruction Process in GaAs

ABSTRACTA new GaAs semiempirical potential energy function which utilizes both two-body and three-body contributions has been used to evaluate the surface energy and surface stress tensor for the (111) and (001)(As-terminated) surfaces as well as for ledges on the (001) surface. Both surface and ledge reconstruction patterns appear to be driven by stress tensor considerations and a long range ledge-ledge interaction arises via the stress tensor. The impact of this finding on two dimensional cluster formation and nucleation at the growing surface is very substantial.

A Structural Analysis of Thin Amorphous Silicon Films

AbstractUsing a semiempirical potential energy function for Si, thin amorphous films of Si have been simulated on crystalline Si by a partial melting and subsequent quenching process. After relaxation at 450°K, the dominant structural feature was a dense free surface skin with a void layer underneath for both c-Si(100) and c-Si(111) substrates and for film thicknesses up to 16Å. Tetrahedral coordination was maintained throughout the amorphous region and structural differences were noted in the α-Si/c-Si interface region for the two orientations considered.