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

Supported Parameters

Atoms:

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

Bonds:

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

Forces:

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

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 (no cutoff)	2.5 fs	175 μs	1250 ns/day	$O(n^2)$	GPU	GPU
Molecular Dynamics	2.5 fs	375 μs	550 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. This term is around the compute cost of biomolecular force fields (e.g. AMBER). However, GPU hardware allows several thousand calculations to occur each clock cycle. This fact makes MM4 much faster than CPU-based simulators (GROMACS, LAMMPS) running the same type of force field.

NOTE: There is currently a massive bottleneck in the $O(n)$ term for nonbonded forces. It makes MM4 roughly 3x slower than it should be. The current performance of MM4 w/ GPU could equate to GROMACS w/ CPU, until the bottleneck is fixed.

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

Linker

MM4 needs to link against OpenMM, which can be problematic for the Swift compiler. On Unix platforms, the easiest method is by setting the environment variable, OPENMM_LIBRARY_PATH. This activates a piece of code in the package manifest for swift-openmm. On Windows (especially through the VSCode terminal), this does not work. An alternative is to modify your VSCode project's package manifest. Copy OpenMM.dll into the same folder as Package.swift, then explicitly link it in the manifest:

targets: [
  .executableTarget(
    name: "CLI",
    dependencies: [
       // Also add other necessary dependencies, such as 'HDL'.
      .product(name: "MM4", package: "MM4"),
    ],
    linkerSettings: [
      // In this example, the computer's user is 'username'. The
      // package manifest is located in the folder 'workspace'.
      .unsafeFlags(["-LC:/Users/username/Documents/.../workspace"]),
      .linkedLibrary("OpenMM"),
    ]),
],