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Sub-atomic Modeling (Mechanics) Calculation of favored (most reduced vitality) sub-atomic structure and vitality taking into account standards of established (Newtonian) material science

Atomic Modeling Part I. A Brief Introduction to Molecular Mechanics

Molecular Modeling (Mechanics) Calculation of favored (least vitality) sub-atomic structure and vitality in view of standards of established (Newtonian) material science "Steric vitality" in light of vitality augmentations because of deviation from some "perfect" geometry Components incorporate security extending, security point bowing, torsional edge misshapening, dipole-dipole communications, van der Waals powers, H-holding and different terms.

Components of "Steric Energy" E steric = E extend + E twist + E torsion + E vdW + E extend twist + E H-holding + E electrostatic + E dipole-dipole + E other

Bond Stretching Energy A Morse potential best portrays vitality of bond extending (& pressure), however it is excessively perplexing for proficient figuring and it requires three parameters for every bond. n (l) = D e {1-exp [-a (l - l 0 )]} 2 if: D e = profundity of potential vitality least, a = w ( m/2D e ) where m is the diminished mass and w is identified with the security extending recurrence by w = (k/m )

Morse potential & Hooke's Law Most securities go astray long next to no from their balance values, so less difficult scientific expressions, for example, the consonant oscillator (Hooke's Law) have been utilized to display the security extending vitality: n (l) = k/2(l - l 0 ) 2

Bond Stretching Energy E extend = k s/2 (l - l 0 ) 2 (Hooke's law constrain... symphonious oscillator) graph: C-C; C=O

Higher request terms give better fit With cubic and higher terms: n (l) = k/2(l - l 0 ) 2 [1-k'(l - l 0 ) -k''(l - l 0 ) 2 -k'''(l - l 0 ) 3 - … ] (cubic terms give better fit in locale close least; incorporation of a fourth power term kills the most extreme in the cubic fcn.)

Bond Angle Bending Energy E twist = k b/2 ( q - q 0 ) 2 chart: sp 3 C-C-C (Likewise, cubic and higher terms are included for better fit with exploratory perceptions)

Torsional Energy Related to the pivot "hindrance" (which additionally incorporates some different commitments, for example, van der Waals communications). The potential vitality increments occasionally as obscuring collaborations happen amid bond revolution. ignoble Eclipsed overshadowed Anti

Torsional Energy E torsion = 0.5 V (1 + cos f ) + 0.5 V 2 (1 + cos 2 f ) + 0.5 V 3 (1 + cos 3 f )

Torsional Barrier in n-Butane

Butane Barrier is Sum of Two Terms: V 1 (1+ cos f) + V 3 (1 + cos 3 f)

van der Waals Energy E vdW = A/r 12 - B/r 6 Lennard-Jones or 6-12 potential blend of a shocking term [A] and an alluring term [B]

van der Waals Energy... E vdW = A (B/r ) - C/r 6 Buckingham potential (basically shock just, particularly at short separations)

Hydrogen Bonding Energy E H-Bond = A/r 12 - B/r 10 (Lennard-Jones sort, with a 10, 12 potential)

Electrostatic Energy E electrostatic = q 1 q 2/c e r ( appealing or unpleasant , relying upon relative indications of charge; esteem depends contrarily on permitivity of free space , or the dielectric steady of the speculative medium)

Dipole-Dipole Energy Calculated as the three dimensional vector aggregate of the security dipole minutes, likewise considering the permitivity (identified with dielectric consistent) of the medium (commonplace default esteem is 1.5) (this is excessively confounded, making it impossible to demonstrate!!!)

Use of Cut-offs Van der Waals strengths, hydrogen holding, electrostatic powers, and dipole-dipole powers have sensational separation conditions; past a specific separation, the drive is irrelevant, yet despite everything it "costs" the PC to compute it. To streamline, "shorts" are regularly utilized for these strengths, normally some place somewhere around 10 and 15å.

Properties Calculated Optimized geometry (least vitality compliance) Equilibrium bond lengths, bond edges, and dihedral (torsional) points Dipole minute (vector whole of bond dipoles) Enthalpy of Formation (in a few projects).

Enthalpy of Formation Equal to "steric vitality" in addition to aggregate of gathering enthalpy values (CH 2 , CH 3 , C=O, and so forth.), with a couple revision terms Not figured by every single sub-atomic workman programs (e.g., HyperChem and Titan ) Calculated qualities are by and large entirely near test values for basic classes of natural mixes.

Enthalpy of Formation...

Enthalpy of Formation...

Bond Lengths Sybyl MM+ MM3 Expt CH 3 CH 3 C-C 1.554 1.532 1.531 1.526 C-H 1.095 1.115 1.113 1.109 CH 3 COCH 3 C-C 1.518 1.517 1.516 1.522 C-H 1.107 1.114 1.111 1.110 C=O 1.223 1.210 1.211 1.222

Bond Angles Sybyl MM+ MM3 CH 3 CH 3 H-C-C 109.5 111.0 111.4 H-C-H 109.4 107.9 107.5 CH 3 COCH 3 C-C-C 116.9 116.6 116.1 H-C-H 109.1 108.3 107.9 C-C-O 121.5 121.7 122.0

Common Force Fields MM2/MM3 (Allinger) best ; broadly useful MMX (Gilbert) included TS's, different components; great MM+ (Ostlund) in HyperChem; general; great OPLS (Jorgenson) proteins and nucleic acids AMBER (Kollman) proteins and nucleic acids + BIO+ (Karplus) CHARMm; nucleic acids MacroModel (Still) biopolymers, general; great MMFF (Merck Pharm.) general; more up to date; great Sybyl in Alchemy2000, general (poor).

Molecular Modeling Programs HyperChem (MM+, OPLS, AMBER, BIO+) Spartan (MM3, MMFF, Sybyl; on SGI or through x-windows from pc) Titan (like Spartan, however speedier; MMFF) Alchemy2000 (Sybyl) Gaussian 03 (on our SGIs linux bunch and on unix PCs at NCSU and ECU; no graphical interface; not for sub-atomic mechanics; MO estimations just)

Steps in Performing Molecular Mechanics Calculations Construct graphical representation of particle to be demonstrated ("front end") Select forcefield technique and end condition (slope, # cycles, or time) Perform geometry advancement Examine yield geometry... is it sensible? Scan for worldwide least.

Energy Minimization Local least versus worldwide least Many nearby minima; one and only worldwide least Methods: Newton-Raphson (piece askew), steepest plummet, conjugate inclination, others. neighborhood minima worldwide least

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