Molecular dynamics implementation cheat sheet
A cheat-sheet for implementing a molecular dynamics simulation
Source: "Nanosystems: Molecular Machinery, Manufacturing, and Computation"
Contents
[hide]- 1 The MM2 model (3.3.2.)
- 2 Bonds under large loads (beyond MM2) (3.3.3.)
- 3 Verlet Integration (not in Nanosystems)
- 4 MM2 vs MM3 (Chapter 3.3.2.g.)
- 5 Bond cleavage & radical coupling (3.4.2)
- 6 Nonbonded & large compression limits (3.3.3.b.)
- 7 Abstraction reactions (Chapter 3.4.3.)
- 8 Continuum models of van der Waals attraction (Chapter 3.5.1.)
- 9 Related
The MM2 model (3.3.2.)
Vs=12ks(r−r0)2[1−kcubic(r−r0)]
Vθ=12kθ(θ−θ0)2[1+ksextic(θ−θ0)4]
ks⊥=kθ/r20
Vω=12[V1(1−cos(1ω))+V2(1−cos(2ω))+V3(1+cos(3ω))]
Vvdw=ϵvdw[2.48×105exp(−12.5rrvdw0)−1.924(rrvdw0)−6]
Vsθ=ksθ(θ−θ0)[(rA−rA0)+(rB−rB0)]
ks,C−C=440N/m
kθ,C−C−C=450zJ/rad2
ϵvdw,Csp3=357yJ
V1,C−C−C−C=1.39zJ, V2,C−C−C−C=1.88zJ, V3,C−C−C−C=0.65zJ
ksθ,C−C−C=1.2nN/rad
kcubic=?m−1
n…nano=10−9
z…zepto=10−21
Bonds under large loads (beyond MM2) (3.3.3.)
Vmorse=De(1−exp[−β(r−r0)]2−1)
Vlippincott=De[1−exp(−ksr0(r−r0)22Der)], r≥r0
For compressive loads Vvdw
Note: Popular Lennard-Jones 6-12 potential is too steep in repulsive regime!
MM2 potential within 10% of experiment for 0.5rvdw
β=√ks/(2De)
De≈D0+ℏ2√ks/μ=D0+ℏω2; μ=m1m2m1+m2
D0
De,C−C=556yJ
Verlet Integration (not in Nanosystems)
→x(t+Δt)=2→x(t)−→x(t−Δt)+→a(t)Δt2+O(Δt4)
→a(t)=m∇→xV(t)
MM2 vs MM3 (Chapter 3.3.2.g.)
★ MM2 prioritizes accuracy in energy and geometry
★ MM3 prioritizes accuracy of vibration frequencies
★ MM3 predicts greater angle-bending stiffness by ~1.5x or more
★ MM3 has a more complex functional form – e.g. it adds:
– stretch-torsion interaction, cubic bending, quartic stretching
★ MM3 has lower energies forces and stiffness in deep repulsive regime by ~10%
★ MM2 overall seems like a more conservative (safe side wrong) choice for diamondoid nanomachinery
Bond cleavage & radical coupling (3.4.2)
The Morse potential Vmorse
Vanti−morse=12De(1+exp[−β(r−r0)]2−1)
But unpaired spins being the limiting factor in reaction rate should
typically be avoidable in piezomechanosynthesis.
See Nanosystems Chapter 8.4.3.b. Radical coupling and intersystem crossing.
Nonbonded & large compression limits (3.3.3.b.)
ks,vdw≈12.5rvdw0Fvdw≈3.5×1010m−1⋅Fvdw
Vvdw≈0.08rvdw0Fvdw≈2.9×10−11m⋅Fvdw
Abstraction reactions (Chapter 3.4.3.)
VLEPS
Continuum models of van der Waals attraction (Chapter 3.5.1.)
Hamaker constant – details omitted here
Related
- Snapback – sideward bond bending stiffness is only 1/20th of radial bond stretching/compressing stiffness
- Energy, force, and stiffness
- Atomic orbitals