The Explicit Hydrogen-Bond Term

The explicit hydrogen-bond energy term $E_{HBON}$ is used in certain parameter sets, in particular the ones that deal with nucleic acids. In the more recent protein parameter files, this term is zero, and the effect of hydrogen bonds is taken implicitly into account by appropriate parameterization of the partial charges and van der Waals parameters. The explicit hydrogen-bond term has the form
$\displaystyle E_{HBON}$ $\textstyle =$ $\displaystyle \sum_{i<j} (\frac{A}{r^{a}_{AD}} - \frac{B}{r^{b}_{AD}})$ (4.25)
    $\displaystyle cos^m(\theta_{A-H-D}) cos^{n} (\theta_{AA-A-H})
SW(r_{AD}^{2},r_{h_{on}}^{2}, r_{h_{off}}^{2})$  
    $\displaystyle SW[cos^{2} (\theta_{A-D-H}), cos^{2}(\theta_{h_{on}}), cos^{2}

involving atoms AA, A, H, D (acceptor antecedent, acceptor, hydrogen, and donor heavy atom), where $a, b, m,$ and $n$ are positive integers and $SW$ is the switching function defined in Eq. 4.9.

The switching function SW maintains a continuous and smooth function to the cutoff point so that derivatives are well defined at the cutoff point. The sum in Eq. 4.25 extends over all pairs of donors and acceptors (DONOr and ACCEptor statements; see Section 3.1.1) for which the donor-acceptor distance and the donor-hydrogen-acceptor angle satisfy the criteria specified by DCUT and ACUT (see Section 3.2.1). AEXP assigns the $b$ exponent, REXP assigns the $a$ exponent, HAEX assigns the $m$ exponent, and AAEX assigns the $n$ exponent; $A$ and $B$ are defined by the HBON statement (see Section 3.2.1). The remaining switching parameters are provided by the hbonds statement. The computational time for searching for hydrogen bonds that satisfy the cutoff criteria is reduced by introducing an approximation, storing the atomic pair indices ($i<j$) that satisfy the cutoff criteria in a list that is updated only when any atom has moved more than the value specified by TOLErance.

Xplor-NIH 2023-11-10