COMPASS force field

COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) is a member of the consistent family of force fields (CFF91, PCFF, CFF and COMPASS), which are closely related second-generation force fields. They were parameterized against a wide range of experimental observables for organic compounds containing H, C, N, O, S, P, halogen atoms and ions, alkali metal cations, and several biochemically important divalent metal cations. PCFF is based on CFF91, extended so as to have a broad coverage of organic polymers, (inorganic) metals, and zeolites. COMPASS is the first force field that has been parameterized and validated using condensed phase properties in addition to various and empirical data for molecules in isolation. Consequently, this forcefield enables accurate and simultaneous prediction of structural, conformational, vibrational, and thermo-physical properties for a broad range of molecules in isolation and in condensed phases.

Functional form

The COMPASS force field (Ref. 1 Eq. 1) consists of terms for bonds (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} ), angles (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} ), dihedrals (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi} ), out-of-plane angles (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi} ) as well as cross-terms, Coulombic charges and a 9-6 non-bonded term

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\mathrm{total}} = E_b + E_{\theta} + E_{\phi} + E_{\chi} + E_{b,b'} + E_{b,\theta} + E_{b,\phi} + E_{\theta,\phi} + E_{\theta,\theta'} + E_{\theta,\theta',\phi} + E_{q} + E_{\mathrm{non-bonded}}}

where

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_b = \sum_b \left[ k_2 (b-b_0)^2 + k_3 (b-b_0)^3 + k_4 (b-b_0)^4 \right]}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\theta} = \sum_{\theta} \left[ k_2 (\theta-\theta_0)^2 + k_3 (\theta-\theta_0)^3 + k_4 (\theta-\theta_0)^4 \right]}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\phi} = \sum_{\phi} \left[ k_1(1-\cos \phi) + k_2(1-\cos 2\phi) + k_3(1-\cos 3\phi) \right]}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\chi} = \sum_{\chi} k_2 \chi^2}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{b,b'} = \sum_{b,b'} k(b-b_0)(b'-b_0')}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{b,\theta} = \sum_{b,\theta} k(b-b_0)(\theta-\theta_0)}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{b,\phi} = \sum_{b,\phi} (b-b_0) \left[k_1 cos \phi + k_2 cos 2\phi + k_3 cos 3\phi\right]}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\theta,\phi} = \sum_{\theta,\phi} (\theta-\theta_0) \left[k_1 cos \phi + k_2 cos 2\phi + k_3 cos 3\phi\right]}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\theta,\theta'} = \sum_{\theta,\theta'} k(\theta-\theta_0)(\theta'-\theta_0')}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\theta,\theta',\phi} = \sum_{\theta,\theta',\phi} k(\theta-\theta_0)(\theta'-\theta_0')\cos \phi}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{q}=\sum_{ij} \frac{q_i q_j}{r_{ij}}}

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{\mathrm{non-bonded}}= \sum_{ij} \epsilon_{ij} \left[ 2 \left(\frac{r_{ij}^0}{r_{ij}} \right)^9 -3 \left(\frac{r_{ij}^0}{r_{ij}} \right)^6\right]}

with the following combining rules (Ref. 1 Eqs. 2 and 3):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_{ij}^0 = \left( \frac{ (r_i^0)^6 + (r_j^0)^6 }{2} \right)^{1/6}}

and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon_{ij} = 2 \sqrt{\epsilon_i \cdot \epsilon_j} \left( \frac{ (r_i^0)^3 \cdot (r_j^0)^3 }{ (r_i^0)^6 \cdot (r_j^0)^6 } \right)}

References

1. H. Sun "COMPASS: An ab Initio Force-Field Optimized for Condensed-Phase Applications - Overview with Details on Alkane and Benzene Compounds", Journal of Physical Chemistry B 102 pp. 7338–7364 (1998)
2. H. Sun, P. Ren and J. R. Fried "The COMPASS force field: parameterization and validation for phosphazenes", Computational and Theoretical Polymer Science 8 pp. 229-246 (1998)
3. S. W. Bunte and H. Sun "Molecular Modeling of Energetic Materials: The Parameterization and Validation of Nitrate Esters in the COMPASS Force Field", Journal of Physical Chemistry B 104 pp. 2477-2489 (2000)
4. Jie Yang, Yi Ren, An-min Tian and Huai Sun "COMPASS Force Field for 14 Inorganic Molecules, He, Ne, Ar, Kr, Xe, H2, O2, N2, NO, CO, CO2, NO2, CS2, and SO2, in Liquid Phases", Journal of Physical Chemistry B 104 pp. 4951-4957 (2000)
5. Michael J. McQuaid, Huai Sun and David Rigby "Development and validation of COMPASS force field parameters for molecules with aliphatic azide chains", Journal of Computational Chemistry 25 pp. 61-71 (2004)