Molecular Modeling

ν(l) = k/2(l - l0)2
Bond Stretching Energy
Bond Stretching Energy
Estretch = ks/2 (l - l0)2
Energy, kcal/mol
350 300 250 200 150 100 50 0 0 1 2 3 Internuclear Distance
2 1.5 1 0.5 0 0 -0.5 1 2 3 4
LennardLennard-Jones or 6-12 potential
combination of a repulsive term [A] and an attractive term [B]
Nonbonded Internuclear Distance
Enthalpy of Formation
Equal to “steric energy” plus sum of group enthalpy values (CH2, CH3, C=O, etc.), with a few correction terms Not calculated by all molecular mechanics programs (e.g., HyperChem and Titan) Titan) Calculated values are generally quite close to experimental values for common classes of organic compounds.
7
Kcal / mol
6 5 4 3 2 1 0 0 30 60 90 120 150 180 210 240 270 300 330 360
Torsion Angle
Butane Barrier is Sum of Two Terms: V1(1+ cos φ) + V3(1 + cos 3φ)
CH3
CH3
H
CH3 CH3 H
H
gauche H
HCH3
H
HH
Eclipsed
H CH3
H
H
HH
eclipsed
H
CH3
H
Anti
CH3
H
Torsional Energy
Etorsion = 0.5 V1 (1 + cos φ) + 0.5 V2 (1 + cos 2φ) + 2φ 0.5 V3 (1 + cos 3φ) 3φ
Molecular Modeling
Part I. A Brief Introduction to Molecular Mechanics
Molecular Modeling (Mechanics)
Calculation of preferred (lowest energy) molecular structure and energy based on principles of classical (Newtonian) physics “Steric energy” based on energy increments due to deviation from some “ideal” geometry Components include bond stretching, bond angle bending, torsional angle deformation, dipoledipole-dipole interactions, van der Waals forces, H-bonding and other terms. H-
Properties Calculated
Optimized geometry (minimum energy conformation) Equilibrium bond lengths, bond angles, and dihedral (torsional) angles Dipole moment (vector sum of bond dipoles) Enthalpy of Formation (in some programs).
Use of Cut-offs
Van der Waals forces, hydrogen bonding, electrostatic forces, and dipole-dipole dipoleforces have dramatic distance dependencies; beyond a certain distance, the force is negligible, yet it still “costs” the computer to calculate it. To economize, “cut-offs” are often “cutemployed for these forces, typically somewhere between 10 and 15Å.
(cubic terms give better fit in region near minimum; inclusion of a fourth power term eliminates the maximum in the cubic fcn.)
Bond Angle Bending Energy
0 106
108
110
112
Bond Angle
Torsional Energy
Related to the rotation “barrier” (which also includes some other contributions, such as van der Waals interactions). The potential energy increases periodically as eclipsing interactions occur during bond rotation.
Bond Angle Deformation, C-C-C
Ebend = kb/2 (θ - θ0)2 (θ
Energy, kcal/mol
35 30 25 20 15 10 5
graph: sp3 C-C-C
(Likewise, cubic and higher terms are added for better fit with experimental observations)
Energy, kcal/mol
Electrostatic Energy
1 0.8 0.6 0.4 0.2 0 -0.2 0 -0.4 -0.6 -0.8 -1 Internuclear Distance 1 2 3 4
Dipole-Dipole Energy
Calculated as the three dimensional vector sum of the bond dipole moments, also considering the permitivity of the medium (typical default value is 1.5) (this is too complicated to demonstrate!!!)
2.5 2 Energy 1.5 1 0.5 0 0 30 60 90 120 150 180 210 240 270 300 330 360 Torsion Angle
van der Waals Energy
van der W aals Energy
2.5
EvdW = A/r12 - B/r6
Energy, kcal/mol
van der Waals Energy...
Buckingham Potential
9
EvdW = A (B/r ) - C/r6
Energy, kcal/mol
8 7 6 5 4 3 2 1 0 0 1 2 3 4 Nonbonded Internuclear Diatance
Buckingham potential (essentially repulsion only, especially at short distances)
Electrostatic Energy
E electrostatic = q1q2 / cε r cε (attractive or repulsive, repulsive, depending on relative signs of charge; value depends inversely on permitivity of free space, space, or the dielectric constant of the hypothetical medium)
2 1.8 1.6 1.4 1.2 Energy 1 0.8 0.6 0.4 0.2 0 0 30 60 90 120 150 180 210 240 270 300 330 360 Torsion Angle
2 1.8 1.6 1.4 1.2 Energy 1 0.8 0.6 0.4 0.2 0 0 30 60 90 120 150 180 210 240 270 300 330 360 Torsion Angle
(Hooke’s law force... harmonic oscillator) graph: C-C; C=O C-
Higher order terms give better fit
With cubic and higher terms: ν(l) = k/2(l - l0)2 [1- k’(l - l0) [1- k’’(l - l0)2 - k’’’(l - l0)3 - …]
Morse potential & Hooke’s Law