philipturner / MM4

Molecular mechanics simulator for molecular nanotechnology

MM4

Molecular Mechanics force field, version 4. The simulator used to create Nanosystems (1992), but updated with modern ab initio parameters.

Documentation: philipturner.github.io/MM4

Atoms

Officially supported:

Element	Ring Types
H	n/a
C	5, 6
Si	5, 6
P (trivalent)	5, 6
S	5, 6
Ge	5, 6

Experimental:

Element	Ring Types
N (trivalent)	5, 6
O	5, 6
F	n/a

Bonds

Officially supported:

Element	H	C	Si	Ge
C	X	X	X	X
Si	X	X	X
P		X
S		X
Ge	X	X

Experimental:

Element	H	C	Si	Ge
N		X
O		X
F		X
Ge				X

Forces

Officially supported:

• bend
• external
• nonbonded
  • van der Waals force
  • overlap repulsion
  • electrostatic force
• stretch
• stretch-bend

Experimental:

• bend-bend
• stretch-stretch
• torsion
• torsion-bend
• torsion-stretch

Levels of Theory

MM4 offloads all molecular dynamics calculations to OpenMM. Rigid body dynamics must be integrated on the CPU by the library user. Any communication between CPU and GPU causes a latency bottleneck. This bottleneck manifests as a large $O(1)$ term in the polynomial for algorithmic complexity.

	Stable Time Step	Minimum Latency/Step	Maximum ns/day	Scaling	Force Computation	Integration
Molecular Dynamics (w/o cutoff)	4.35 fs	100 μs	3200 ns/day	$O(n^2)$	GPU	GPU
Molecular Dynamics (w/o neighbor list)	4.35 fs	200 μs	1600 ns/day	$O(n^2)$	GPU	GPU
Molecular Dynamics	4.35 fs	700 μs	500 ns/day	$O(n)$	GPU	GPU
Rigid Body Dynamics	80 fs	1500 μs	4000 ns/day	$O(n)$	GPU	CPU

For large atom counts and lower-end hardware, the $O(n)$ term will dominate. It is about the compute cost of biomolecular force fields (e.g. AMBER). However, GPU hardware allows several thousand calculations to occur each clock cycle. This makes MM4 much faster than CPU-based simulators (GROMACS, LAMMPS) running the same type of force field.

Units

MM4 and OpenMM use slightly different unit systems. MM4 adheres to the SI system: nanometer, yoctogram, picosecond. Units for force and energy are derived from dimensional analysis.

energy = m * v^2 = yg * (nm/ps)^2 = zJ
force = dU / dx = zJ / nm = pN

Unit	MM4	OpenMM
Angle	rad	rad
Energy	zJ	kJ/mol
Force	pN	kJ/mol/nm
Mass	yg	amu
Length	nm	nm
Speed	nm/ps	nm/ps
Time	ps	ps

Value in SI Units	SI Unit	MM4	OpenMM
Angle	rad	1	1
Energy	J	1e-21	1.66e-21
Force	N	1e-12	1.66e-12
Mass	kg	1e-27	1.66e-27
Length	m	1e-9	1e-9
Speed	m/s	1000	1000
Time	s	1e-12	1e-12