Contacts

coordNum: coordination number between two groups.

The coordNum {...} block defines a coordination number (or number of contacts), which calculates the function $(1-(d/d_0)^{n})/(1-(d/d_0)^{m})$ , where $d_0$ is the ``cutoff'' distance, and $n$ and $m$ are exponents that can control its long range behavior and stiffness [49]. This function is summed over all pairs of atoms in group1 and group2:

$$C (\mathtt{group1}, \mathtt{group2}) \; = \; \sum_{i\in\mathtt{gr... ...}\vert/d_{0})^{n}}{ 1 - (\vert\mathbf{x}_{i}-\mathbf{x}_{j}\vert/d_{0})^{m} } }$$ (13.3)

List of keywords (see also for additional options):

• group1: see definition of group1 (distance component)

• group2: analogous to group1

• cutoff $\langle\,$ ``Interaction'' distance (Å)$\,\rangle$
  Context: coordNum
  Acceptable values: positive decimal
  Default value: 4.0
  Description: This number defines the switching distance to define an interatomic contact: for $d \ll d_0$ , the switching function $(1-(d/d_0)^{n})/(1-(d/d_0)^{m})$ is close to 1, at $d = d_0$ it has a value of $n/m$ ($1/2$ with the default $n$ and $m$ ), and at $d \gg d_0$ it goes to zero approximately like $d^{m-n}$ . Hence, for a proper behavior, $m$ must be larger than $n$ .

• cutoff3 $\langle\,$ Reference distance vector (Å)$\,\rangle$
  Context: coordNum
  Acceptable values: ``(x, y, z)'' triplet of positive decimals
  Default value: (4.0, 4.0, 4.0)
  Description: The three components of this vector define three different cutoffs $d_{0}$ for each direction. This option is mutually exclusive with cutoff.

• expNumer $\langle\,$ Numerator exponent$\,\rangle$
  Context: coordNum
  Acceptable values: positive even integer
  Default value: 6
  Description: This number defines the $n$ exponent for the switching function.

• expDenom $\langle\,$ Denominator exponent$\,\rangle$
  Context: coordNum
  Acceptable values: positive even integer
  Default value: 12
  Description: This number defines the $m$ exponent for the switching function.

• group2CenterOnly $\langle\,$ Use only group2's center of mass$\,\rangle$
  Context: coordNum
  Acceptable values: boolean
  Default value: off
  Description: If this option is on, only contacts between each atoms in group1 and the center of mass of group2 are calculated (by default, the sum extends over all pairs of atoms in group1 and group2). If group2 is a dummyAtom, this option is set to yes by default.

• tolerance $\langle\,$ Pairlist control$\,\rangle$
  Context: coordNum
  Acceptable values: decimal
  Default value: 0.0
  Description: This controls the pairlist feature, dictating the minimum value for each summation element in Eq. 13.3 such that the pair that contributed the summation element is included in subsequent simulation timesteps until the next pairlist recalculation. For most applications, this value should be small (eg. 0.001) to avoid missing important contributions to the overall sum. Higher values will improve performance by reducing the number of pairs that contribute to the sum. Values above 1 will exclude all possible pair interactions. Similarly, values below 0 will never exclude a pair from consideration. To ensure continuous forces, Eq. 13.3 is further modified by subtracting the tolerance and then rescaling so that each pair covers the range $\left[0, 1\right]$ .

• pairListFrequency $\langle\,$ Pairlist regeneration frequency$\,\rangle$
  Context: coordNum
  Acceptable values: positive integer
  Default value: 100
  Description: This controls the pairlist feature, dictating how many steps are taken between regenerating pairlists if the tolerance is greater than 0.

This component returns a dimensionless number, which ranges from approximately 0 (all interatomic distances are much larger than the cutoff) to $N_{\mathtt{group1}} \times N_{\mathtt{group2}}$ (all distances are less than the cutoff), or $N_{\mathtt{group1}}$ if group2CenterOnly is used. For performance reasons, at least one of group1 and group2 should be of limited size or group2CenterOnly should be used: the cost of the loop over all pairs grows as $N_{\mathtt{group1}} \times N_{\mathtt{group2}}$ . Setting $\mathtt{tolerance} > 0$ ameliorates this to some degree, although every pair is still checked to regenerate the pairlist.

selfCoordNum: coordination number between atoms within a group.

The selfCoordNum {...} block defines a coordination number similarly to the component coordNum, but the function is summed over atom pairs within group1:

$$C (\mathtt{group1}) \; = \; \sum_{i\in\mathtt{group1}}\sum_{j > i... ...}\vert/d_{0})^{n}}{ 1 - (\vert\mathbf{x}_{i}-\mathbf{x}_{j}\vert/d_{0})^{m} } }$$ (13.4)

The keywords accepted by selfCoordNum are a subset of those accepted by coordNum, namely group1 (here defining all of the atoms to be considered), cutoff, expNumer, and expDenom.

List of keywords (see also for additional options):

• group1: see definition of group1 (coordNum component)
• cutoff: see definition of cutoff (coordNum component)
• cutoff3: see definition of cutoff3 (coordNum component)
• expNumer: see definition of expNumer (coordNum component)
• expDenom: see definition of expDenom (coordNum component)
• tolerance: see definition of tolerance (coordNum component)
• pairListFrequency: see definition of pairListFrequency (coordNum component)

This component returns a dimensionless number, which ranges from approximately 0 (all interatomic distances much larger than the cutoff) to $N_{\mathtt{group1}} \times (N_{\mathtt{group1}} - 1) / 2$ (all distances within the cutoff). For performance reasons, group1 should be of limited size, because the cost of the loop over all pairs grows as $N_{\mathtt{group1}}^2$ .

hBond: hydrogen bond between two atoms.

The hBond {...} block defines a hydrogen bond, implemented as a coordination number (eq. 13.3) between the donor and the acceptor atoms. Therefore, it accepts the same options cutoff (with a different default value of 3.3 Å), expNumer (with a default value of 6) and expDenom (with a default value of 8). Unlike coordNum, it requires two atom numbers, acceptor and donor, to be defined. It returns an adimensional number, with values between 0 (acceptor and donor far outside the cutoff distance) and 1 (acceptor and donor much closer than the cutoff).

List of keywords (see also for additional options):

• acceptor $\langle\,$ Number of the acceptor atom$\,\rangle$
  Context: hBond
  Acceptable values: positive integer
  Description: Number that uses the same convention as atomNumbers.
• donor: analogous to acceptor
• cutoff: see definition of cutoff (coordNum component)
  Note: default value is 3.3 Å.
• expNumer: see definition of expNumer (coordNum component)
  Note: default value is 6.
• expDenom: see definition of expDenom (coordNum component)
  Note: default value is 8.