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In stead, these m eth od s solve the poten tial energy surface by using a force field equation (see Molecular Mechanics" on page2] i.The force field equation represen ts electron ic energy implicitly th roil gh param eteri/ation. 

Ifnited atom force fields (see Ifnited versiisAll Atom Forcehiclds" on page 28 ) arc sometimes used for bioraoleciiles to decrease the number of nonbonded in teraction s and the computation time. Another reason for using a simplified poten tial is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

Example Crippen and Snow reported their success in developing a simplified potential for protein folding. In their model, single poin Ls rep resell t am in o acids. For th e avian pan creatic polypeptide, th c n ative structure is not at a poten tial m in imum. However, a global search fotin d that the most stable poten tial m in im urn h ad only a 1.8, An gstrom root-m ean-square deviation from thenative structu re. 

Molecu lar mechari ical force fields use the equation s of classical mech an ics to describe th e poteri tial energy surfaces and physical properties of m olecii Ies. A molecu le is described as a collection of atom slhal in teracl with each other by sim pic an alytical fiiriclions. I h is description is called a force field. One component of a force field is th e eri ergy arisiri g from com pression and stretch in g a bond. 

Th e bon ding between two atom s is an alogoiis to a sprin g conn ect-ing two rn asses, L siri g th is an alogy, equation 7 gives the poten tial energy ol the system of masses, and the force constant of... 

Example For the AMEER force field, a carbonyl C-0 bond has an eqnilibrniin bond length of 1.229 A and a force con stant of 570 kcal/mol A-. The potential for an aliphatic C-C bond has a in ini-mum at 1.526 A. I hc slope of the latter poten tial is less steep a C... 

The relative sizes ofthe poten tial barriers in dicate that the AF force con Stan t is larger th an the V con stan t. fh e ph ase sh ift is 180 degrees for th e Fourier compoiien t with a two-fold barrier. Minima occur at 180, 0, and I 80 degrees and maxima at 90 and 90... 

The Extended Iliickel method, for example, does not explicitly consider the elTects of electron-electron repulsions but incorporates rep 11 Ision s into a sin gle-clectron poten tial. Th is simplifies th c solution of the Schrbdinger equation and allows IlyperChem to compute the poten tial energy as the sum of the energies for each electron. 

Th c classical clccirostatic polcri tial for poin t, cti argcs is iti c polCTitial energy at a position Ktccjuation 18). 

For a poten tial energy V and Cartesian coordinates r,. the opti-mi/ed coordinates satisfy this equation ... 

Ch aracteri/e a poten tial en ergy m in im u m. A geom etry optim i-zalioti results in a new structure at a m in itn urn. You can examine atomic coordinates and energy of this slruetiire. 

Th c Newton-Raph son block dingotial method is a second order optim izer. It calculates both the first and second derivatives of potential energy with respect to Cartesian coordinates. I hese derivatives provide information ahont both the slope and curvature of lh e poten tial en ergy surface, Un like a full Newton -Raph son method, the block diagonal algorilh m calculates the second derivative matrix for one atom at a lime, avoiding the second derivatives with respect to two atoms. 

I he eigenvector-following (or Hessian mode) method implemented in HyperChem is based on an effieien t quasi-Newton like algorithm for loca tin g tran sitiori states, wh ieh can locate tran si-tion states for alternative rearran gern eri t/dissoeiation reactions, even when startin g from th e wron g regio n on th e poten tial en ergy surface. 

Molecular clynainics sim illations calculate future position s and velocities of atoms, based on their current positions and velocities. A sim Illation first determ in es the force on each atom (lY) as a function of time, ct ual to the negative gradient of the polen tial en ergy (ct]uation 2 I ),... 

Th c total en ergy of th e system. called the Hamilton iari, is ih c sum of th e kin elic an d poten tial energies (equation 24). 

Because of liiTi itation s iu corn pu ter poxver an d time, it is frequen tly impractical to run a constant energy molecular dynaniics simulation. -Several approxirn ation s to th e eu ergy (usually to th e poteu -tial en ergy) are possible, wh ieh require m odifyiri g th e Ham ilto-... 

Ovcrcom c poten tial energy harriers an d force a m oiecule in to a lower cn ergy con form ation th an th e on e you m igh t obtain using geometry optim i/.ation alone. 

L se a shifted function only to reproduce reported results. Since a sh ifted dielecinc poteniial affects th e entire poten tial energy surface, it is not recommended. 

You need to specify two parameters the et uilibrium value ofthe internal coordinate and the force constant for the harmonic poten tial, T h e equilibrium restraint value deperi ds on the reason you choosea restraint. If, for example, you would like a particular bond length to remain constant during a simulation, then the equ ilibritirn restrain t value would probably be Lh e initial len gth of the bond. If you wan t to force an internal coordinate to a new value, the equilibrium internal coordinate is the new value. 

The INDO meth od (In termediate N DO) corrects some of the worst problems with CNDO. Tor example, INDO exchange integrals between electrons on the same atom need not he eL tial, hut can depend on the orbitals involved. Though this introduces more parameters, additional compulation time is negligible. INDO and MINDO/11 (.Vlodilied INDO, version II) methods are different im piemen lalion s of the same approxim ation. ... 

ZINDO/1 IS based on a modified version of the in termediate neglect of differen tial overlap (IXDO), which was developed by Michael Zerner of the Quantum Theory Project at the University of Florida. Zerner s original INDO/1 used the Slater orbital exponents with a distance dependence for the first row transition metals only. Ilow ever. in HyperChein constant orbital expon en ts are used for all the available elein en ts, as recommended by Anderson. Friwards, and Zerner. Inorg. Chem. 2H, 2728-2732.iyH6. 

TheLUMO oT phcn yIcth ylcn c also has most den siLy at thetenni-Tial (betai carbon, so that these two atoms attach to each other, yielding the sterically unfavorable product. 

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