Hydrogen bonds -------------- | :ref:gmx hbond  | The program :ref:gmx hbond  analyzes the *hydrogen bonds* (H-bonds) between all possible donors D and acceptors A. To determine if an H-bond exists, a geometrical criterion is used, see also :numref:Fig. %s : .. math:: \begin{array}{rclcl} r & \leq & r_{HB} & = & 0.35~\mbox{nm} \\ \alpha & \leq & \alpha_{HB} & = & 30^o \\ \end{array} :label: eqnhbondgeomtric .. _fig-hbond: .. figure:: plots/hbond.* :width: 7.50000cm Geometrical Hydrogen bond criterion. The value of :math:r_{HB} = 0.35 \mathrm{nm} corresponds to the first minimum of the RDF of SPC water (see also :numref:Fig. %s ). The program :ref:gmx hbond  analyzes all hydrogen bonds existing between two groups of atoms (which must be either identical or non-overlapping) or in specified donor-hydrogen-acceptor triplets, in the following ways: .. _fig-hbondinsert: .. figure:: plots/hbond-insert.* :width: 7.50000cm Insertion of water into an H-bond. (1) Normal H-bond between two residues. (2) H-bonding bridge via a water molecule. - Donor-Acceptor distance (:math:r) distribution of all H-bonds - Hydrogen-Donor-Acceptor angle (:math:\alpha) distribution of all H-bonds - The total number of H-bonds in each time frame - The number of H-bonds in time between residues, divided into groups :math:n-:math:n\ +\ :math:i where :math:n and :math:n\ +\ :math:i stand for residue numbers and :math:i goes from 0 to 6. The group for :math:i=6 also includes all H-bonds for :math:i>6. These groups include the :math:n-:math:n\ +\ :math:3, :math:n-:math:n\ +\ :math:4 and :math:n-:math:n\ +\ :math:5 H-bonds, which provide a measure for the formation of :math:\alpha-helices or :math:\beta-turns or strands. - The lifetime of the H-bonds is calculated from the average over all autocorrelation functions of the existence functions (either 0 or 1) of all H-bonds: .. math:: C(\tau) ~=~ \langle s_i(t)~s_i (t + \tau) \rangle :label: eqnhbcorr - with :math:s_i(t) = \{0,1\} for H-bond :math:i at time :math:t. The integral of :math:C(\tau) gives a rough estimate of the average H-bond lifetime :math:\tau_{HB}: .. math:: \tau_{HB} ~=~ \int_{0}^{\infty} C(\tau) d\tau :label: eqnhblife - Both the integral and the complete autocorrelation function :math:C(\tau) will be output, so that more sophisticated analysis (*e.g.* using multi-exponential fits) can be used to get better estimates for :math:\tau_{HB}. A more complete analysis is given in ref. \ :ref:173 ; one of the more fancy option is the Luzar and Chandler analysis of hydrogen bond kinetics \ :ref:174 , :ref:175 . - An H-bond existence map can be generated of dimensions *# H-bonds*\ :math:\times\ *# frames*. The ordering is identical to the index file (see below), but reversed, meaning that the last triplet in the index file corresponds to the first row of the existence map. - Index groups are output containing the analyzed groups, all donor-hydrogen atom pairs and acceptor atoms in these groups, donor-hydrogen-acceptor triplets involved in hydrogen bonds between the analyzed groups and all solvent atoms involved in insertion.