Closed-Shell Repulsion Coulomb InteractionFrontier Orbital Interaction-unocc.unocc. occ.occ.ssrEr - Es2(!abcracsb"ab)2!!!!+!k<l#RklQkQlab(qa + qb)"abSab +!$E = -rChem 1140; Molecular Modeling• Molecular Mechanics• Semiempirical QM Modeling• CaCHEA. Modeling SoftwareOverview: http://cmm.info.nih.gov/software.html- CaCHe: Structure building. Extended MM2(87)energy minimization, extended Hückel, MOPAC,ZINDO MO programs. Orbital electron density andelectrostatic maps. Prediction of octanol/waterpartition coefficient and water solubilityP. Wipf 1 Chem 1140B. Introduction to Molecular ModelingObjectives:- Computer graphics visualization of molecules ("Dreiding models")- Matching (overlays, docking) of molecules- Use of empirical force-fields to determine molecular properties aswell as interatomic distances.- Correlate molecular properties with an electronic structure fromab initio quantum mechanics or semiempirical quantum mechanics.- Gain information on dynamic molecular movements.- Use computer-assisted design for molecular recognition in organic, bioorganic, and medicinal chemistry and material science.P. Wipf 2 Chem 1140Schematic of molecular force field expression. Diagonal terms refer to interactions that can be expressed as functions of a single internal coordinate, whereas cross terms introduce coupled interactions involving two or more coordinates. P. Wipf 3 Chem 1140Computational OptionsP. Wipf 4 Chem 1140In local methods for finding a minimum effort is directed toward a nearby local minimum, and steps that may increase the function are not permitted. Descent structure of local minimization algorithms: P. Wipf 5 Chem 1140P. Wipf 6 Chem 1140! - Grid search; For very simple structures, this can be do ne manually. (MM2/3: angle driver to create reasonable starting geometries for conformational searching). HHHHHHHHHH" This systematic procedure provides guaranteed coverage of all regions of space if a sufficient number of starting points is selected (at least 3 per dihedral angle). Problems: an extraordinary large number of starting structures is generated, which renders the problem very computer-time intensive, especially for flexible structures. For example, for polypeptides of n residues, a rough range of 10n to 25n reasonable starting points by coarse subdomain partition of backbone and sidechains have to be investigated. If the number of values of for each torsion is reduced, the resolution with which space is covered may be inadequate to provide a starting geometry in the vicinity of each minimum. P. Wipf 7 Chem 1140(1 a.u. = 627.510 kcal/mol) Force Field Eq. (kcal/mol) Ax. (kcal/mol) (kcal/mol) MM3/92 9.10 10.87 1.77 Chem3D (MM2) 6.90 8.67 1.77 CaCHe (MM2?) 6.89 8.68 1.79 MM2* 6.89 8.67 1.78 MM3* 9.10 10.87 1.77 Amber* 1.84 2.87 1.03 OPLS* 0.78 2.57 1.79 Sybyl (tripos) 1.30 2.70 1.40 Sybyl (Spartan) 1.30 2.70 1.40 MMFF (Spartan) 0.70 2.07 1.37 Exp. 1.74 MNDO -36.19 -35.16 1.03 AM1 -43.70 -42.28 1.42 PM3 -36.87 -35.75 1.12 STO-3G E(HF) -270.063379 a.u. -270.060444 a.u. 1.84 6-31G* E(HF) -273.2436640 a.u. -273.2399991 a.u. 2.30 6-31+G* E(HF) -273.245892 a.u. -273.242122 a.u. 2.37 6-311+G** E(HF) -273.308789 a.u. -273.305906 a.u. 1.81 DFT/LSDA/VWN -272.6182101 a.u. -272.6149537 a.u. 2.04 The ab initio calculation at the 6-311+G** E(HF) level required 1,800 x more time than MM2. C. Semiempirical MethodsMolecular mechanics methods are based on classical concepts and requirecomputer time roughly proportional to the square of the number of atoms. Incontrast, semiempirical methods at the Hartree-Fock level use acombination of quantum chemical models and experimentally determinedparameters to strive for accuracy and scale up as (4N)3. Finally, ab initioquantum mechanics proceeds as (10N)4 (for glucose: 1:1,500:6,000,000).There are important differences between classical molecular mechanicsand quantum mechanical methods. MM methods are extremely fast andable to handle very large systems. Particularly for hydrocarbons, they arealso as accurate as the best ab initio methods. But they are onlyparametrized for ground state systems and common bonding situations(functional groups). MM methods are unable to anticipate the making andbreaking of most bonds, the electronic properties of molecules, and thechemistry of electronically excited states.P. Wipf 8 Chem 1140Use molecular orbital methods to compute:- bond orders- dipole moments- ionization potentials- vibrational frequencies and IR, UV spectra- MO energies- partial charges- potential energy maps- reaction pathways- transition states- heats of formation- mapping bond breaking and bond formationThe transition between semiempirical and ab initio quantum chemistry isnot always obvious. Basis sets, for example, are empirical in nature, asare effective core potentials.P. Wipf 9 Chem 1140P. Wipf 10 Chem 1140AM1: - seems to be most accurate for calculations of dipole moments for elements that it has been parametrized for. - reproduces hydrogen-bonds slightly better and - gives energies that are still too large for activation barriers. - reproduces ground-state geometries quite accurately. - is poor in reproducing lon-pair lon-pair repulsion. - has an average error of heats of formation of C, H, N, O compounds of ca. 40%. Characterizations of the wave function In a se mi-empirical calculation, the energy, the first derivatives of the energy and the wave function for the molecule are computed. Other molecular properties are basically an average over the wave function of certain operators describing the properties. Among the visualizable properties that are generally computed are: Total electron density represents the probability of an electron being at a particular point in space. Spin density defines the excess probability of finding spin-up over spin-down electrons at a point in space. The spin density at the position of a nucleus is the a prime determinant of ESR spectra. Orbital plots are used to vi sualize molecular orbitals, especially frontier orbitals, for the analysis of organic reactions. Electrostatic potentials can be used to predict initial attack positions of ions during a reaction. The potential of a positive probe charge is calculated as a function of the distance to the molecule, the nuclear